8.8比例查找尺寸

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  比例查找尺寸

  

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  Sarah is at a miniature exhibit. There is a model of a skyscraper. Underneath the model was a ratio. It said:
  ::Sarah正在参加一个小型展览。有一个摩天大楼的模型。在模型的底部是比例。它说:

  $$\begin{array}{r}1\text{ inch}=30\text{ feet}.\end{array}$$

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  If the model is 38 inches tall, how Sarah use this information to find the actual height of the skyscraper?
  ::如果模型是38英寸高, 莎拉如何使用这些信息 找到摩天大楼的实际高度?

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  In this concept, you will learn how proportions are used to find actual and scale  dimensions  using a scale ratio.
  ::在这个概念中,你将了解如何使用比例来使用一个比额表比率来找出实际的和规模的维度。

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  Using Proportions to Find Dimensions
  ::使用比例来查找尺寸

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  A  scale  is a ratio that shows the relationship between the representation of an object and the real measurement of an object. Toy makers use scale ratios to make models of cars and airplanes that are proportional to the real thing. Architects use scale drawings to plan the design of buildings.
  ::比例尺是显示物体表示与物体实际测量之间关系的比例。 玩具制造商使用比例尺比来制作与真实事物成比例的汽车和飞机模型。 建筑师使用比例尺图来规划建筑物的设计。

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  A  scale drawing  is a drawing that is used to represent and object that is too large to be drawn in its actual dimensions. If a drawing is to scale, you can use proportions to determine the actual dimensions of the scale drawing.
  ::比例尺绘图是指用于表示和表达实际尺寸太大而无法绘制的图纸。如果绘图是比例尺,可以使用比例尺来确定比例尺的实际尺寸。

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  Let’s look at a scale drawing of a sculpture. In the drawing, the sculpture is 4 inches tall. The scale is 1 inch : 4 feet. It scale can be written as
  ::让我们看看雕塑的刻度图画。 在绘画中,雕塑高4英寸。 缩幅是1英寸: 4英尺。 缩幅可以写成

  $$\begin{array}{r}\frac{1\text{ in}}{4\text{ ft}}\end{array}$$

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  (Note: Inch is abbreviated “in.” or with the double prime mark, ″. Foot/feet is abbreviated “ft” or with the single prime mark, ′.)
  ::注: Inch 缩写为“ in ” , 或以双正值表示, 。 foot/ feet 缩写为“ft ” , 或以单正值表示 。 )

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  A drawing with this scale tells you that 1 inch on paper is equal to 4 feet in real life. If the drawing is 4 inches tall, use the scale to find the actual height of the sculpture.
  ::这个比例尺的绘图告诉您纸上1英寸等于实际生活中的4英尺。 如果画高4英寸, 请使用这个比例尺来找到雕塑的实际高度 。

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  First, create a  proportion  using  equivalent ratios . Remember to write the corresponding units in the numerator and in the denominator. The actual height of the sculpture is represented by the  variable   $\begin{array}{r}x\end{array}$ .
  ::首先,使用等值比例创建比例。 记住在分子和分母中写入相应的单位。 雕塑的实际高度由变量 x 表示 。

  $$\begin{array}{r}\frac{1\text{ in.}}{4\text{ ft.}}=\frac{4\text{ in.}}{x\text{ ft.}}\end{array}$$

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  Then, cross multiply and simplify the  equation  to find the value of  $\begin{array}{r}x\end{array}$ .
  ::然后,交叉乘并简化方程式以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}x& =& 4(4)\\ x& =& 16\end{array}\end{array}$$

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  The sculpture will be 16 feet tall.
  ::雕塑将达到16英尺高

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  Let’s make a scale drawing. Use the scale  $\begin{array}{r}{1}^{\mathrm{\prime }\mathrm{\prime }}=2^{\mathrm{\prime }}\end{array}$ . Draw a room that is  $\begin{array}{r}{8}^{\mathrm{\prime }}\times {12}^{\mathrm{\prime }}\end{array}$ .
  ::让我们绘制一个比例尺。 请使用比例尺 1 = = 2 = 。 请绘制一个房间为 8 = 12 = 。

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  First, write a proportion to find the measurement of the width.
  ::首先,写一个比例以找到宽度的测量值。

  $$\begin{array}{r}\frac{1^{\mathrm{\prime }\mathrm{\prime }}}{2^{\mathrm{\prime }}}=\frac{x^{\mathrm{\prime }\mathrm{\prime }}}{8^{\mathrm{\prime }}}\end{array}$$

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  Next, cross multiply and simplify the equation to find the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,交叉乘并简化方程以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}2x& =& 1(8)\\ 2x& =& 8\\ x& =& 4\end{array}\end{array}$$

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  The drawing will be 4 inches wide.
  ::画的宽度是4英寸

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  Then, write a proportion to find the measurement of the length.
  ::然后,写一个比例 以找到长度的测量。

  $$\begin{array}{r}\frac{1^{\mathrm{\prime }\mathrm{\prime }}}{2^{\mathrm{\prime }}}=\frac{x^{\mathrm{\prime }\mathrm{\prime }}}{{12}^{\mathrm{\prime }}}\end{array}$$

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  Finally, cross multiply and simply the equation to find the value of  $\begin{array}{r}x\end{array}$ .
  ::最后,交叉乘数和简单的方程来寻找 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}2x& =& 12\\ x& =& 6\end{array}\end{array}$$

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  The drawing will be 6 inches long
  ::绘图将长6英寸

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  In the drawing room will be  $\begin{array}{r}4\text{ inches}\times 6\text{ inches}\end{array}$ . If one unit on the drawing is equal to one inch, here is the room.
  ::客厅内4英寸×6英寸。如果一个单位在绘图上等于1英寸,这里就是房间。

  

  [Figure 2]

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  Scale dimensions are also used to figure out the actual dimensions of something.
  ::规模维度还被用来确定某种事物的实际维度。

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  The flower bed design shows that the width of the garden on the drawing is six inches. If the scale is 1 in. = 5 ft, how wide is the actual flower garden?
  ::花床的设计显示,绘画上的花园宽度是6英寸。如果比例尺是1英寸 = 5英尺,那么实际的花园宽度是多少?

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  First, write a proportion to find the actual measurement of the flower bed.
  ::首先,写一个比例来找到花床的实际测量量。

  $$\begin{array}{r}\frac{1\text{ in.}}{5\text{ ft.}}=\frac{6\text{ in.}}{x\text{ ft.}}\end{array}$$

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  Then, cross multiply and simplify the equation to find the value of  $\begin{array}{r}x\end{array}$ .
  ::然后,交叉乘并简化方程式以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}x& =& 5(6)\\ x& =& 30\end{array}\end{array}$$

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  The actual flower bed is 30 feet wide.
  ::实际的花床宽度是30英尺

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  Examples
  ::实例

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  Example 1
  ::例1

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  Earlier, you were given a problem about Sarah at the miniature exhibit.
  ::早些时候,你在小型展览会上 遇到一个关于莎拉的问题

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  The model is 38 inches tall and it uses the scale  $\begin{array}{r}1\text{ inch}=30\text{ feet}\end{array}$ . To find the actual height, Sarah can use a proportion.
  ::该模型高38英寸,使用1英寸的尺数=30英尺。要找到实际身高,Sarah可以使用比例。

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  First, write a proportion.
  ::首先,写一个比例。

  $$\begin{array}{r}\frac{1\text{ in.}}{30\text{ ft.}}=\frac{38\text{ in.}}{x\text{ ft.}}\end{array}$$

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  Next, cross multiply simplify to find the value of  $\begin{array}{r}x\end{array}$ .
  ::下一步,交叉乘法简化以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}x& =& 30(38)\\ x& =& 1140\end{array}\end{array}$$

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  The actual height of the building is 1,140 feet.
  ::大楼的实际高度为1 140英尺。

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  Example 2
  ::例2

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  Solve the proportion:  $\begin{array}{r}\frac{7\text{ in.}}{70\text{ ft.}}=\frac{x\text{ in.}}{140\text{ ft.}}\end{array}$ .
  ::解决比例:70英尺7英寸=x140英尺。

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  First, cross multiply and simplify to find the value of  $\begin{array}{r}x\end{array}$ .
  ::首先,交叉乘法和简化以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}70x& =& 7(140)\\ 70x& =& 980\\ x& =& 14\end{array}\end{array}$$

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  Or, use mental math to solve for  $\begin{array}{r}x\end{array}$ .
  ::或者用心理数学解答 x。

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  First, look at the relationship between the two given denominators. Think, “The second denominator is double the first denominator.”
  ::首先,看看两个特定分母之间的关系。 想想, “ 第二个分母是第一个分母的两倍 。 ”

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  Then, take the given numerator and multiply by 2. Think, “7 times 2 is 14.”
  ::然后,取给定的分子乘以2。 想想, “7乘以2是14”。

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  The answer is 14 inches.
  ::答案是14英寸

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  Example 3
  ::例3

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  Solve the proportion:  $\begin{array}{r}\frac{1\text{ in.}}{3\text{ ft.}}=\frac{x\text{ in.}}{21\text{ ft.}}\end{array}$ .
  ::解决比例:1英寸 3英尺=x. 21英尺。

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  First, cross multiply and simplify to find the value of  $\begin{array}{r}x\end{array}$ .
  ::首先,交叉乘法和简化以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}3x& =& 21\\ x& =& 7\end{array}\end{array}$$

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  The answer is 7 inches.
  ::答案是7英寸

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  Example 4
  ::例4

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  Solve the proportion:  $\begin{array}{r}\frac{3\text{ in.}}{6\text{ ft.}}=\frac{9\text{ in.}}{x\text{ ft.}}\end{array}$ .
  ::解决比例:3英寸6英尺=9英寸x英尺。

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  First, cross multiply and simplify to find the value of  $\begin{array}{r}x\end{array}$ .
  ::首先,交叉乘法和简化以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}3x& =& 6(9)\\ 3x& =& 54\\ x& =& 18\end{array}\end{array}$$

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  The answer is 18 feet.
  ::答案是18英尺

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  Example 5
  ::例5

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  Find the proportion:  $\begin{array}{r}\frac{2\text{ in.}}{10\text{ ft.}}=\frac{x\text{ in.}}{120\text{ ft.}}\end{array}$ .
  ::查找比例: 10英尺=x. 120英尺。

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  First, cross multiply and simplify to find the value of  $\begin{array}{r}x\end{array}$ .
  ::首先,交叉乘法和简化以找到 x 的值。

  $$\begin{array}{r}\begin{array}{rcl}10x& =& 2(120)\\ 10x& =& 240\\ x& =& 24\end{array}\end{array}$$

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  The answer is 24 inches.
  
  ::答案是24英寸

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  Review
  ::回顾

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  Find the actual dimension.
  ::找到实际的维度。

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  1. The scale of the drawing shows that 1  inch = 5 feet. If the drawing shows the height of the building as 5 inches, how tall is the actual building?
     ::绘图比例显示 1 英寸 = 5 英尺。 如果绘图显示大楼的高度为 5 英寸, 实际建筑的高度是 多少 ?
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  2. Given this scale, a drawing of a building is 7 inches how tall is the actual building?
     ::鉴于这个规模,一栋建筑的图画是7英寸, 实际建筑有多高?
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  3. Given this scale, how tall is a building that has a drawing that is 15 inches?
     ::鉴于这个规模,一个有15英寸的图画的建筑物有多高?
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  4. The scale of the drawing shows that 2 inches = 10 feet. If the drawing shows the height of the building as 8 inches, how tall is the actual building?
     ::绘图比例显示2英寸=10英尺。如果绘图显示建筑物高度为8英寸,那么实际建筑物的高度是多少?
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  5. The scale of the drawing shows that 1 inch = 3 feet. If the drawing shows the height of the tree as 9 inches, how tall is the tree?
     ::绘图比例显示 1 英寸 = 3 英尺。 如果绘图显示树的高度为 9 英寸, 树的高度是 多高 ?
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  6. The scale of the drawing shows that 2 inches = 7 feet. If the drawing shows that the height of the tree is 6 inches, how tall is the tree?
     ::绘图比例显示2英寸=7英尺。如果绘图显示树的高度是6英寸,那么树的高度是多少?
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  7. The scale of the drawing shows that 1 inch = 3 feet. If the drawing shows that the height of the tree house is 3 inches, how high is the actual tree house?
     ::绘图比例显示 1 英寸 = 3 英尺。 如果绘图显示树屋的高度是 3 英寸, 实际的树屋有多高 ?

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  Find the scale dimension.
  ::查找天平尺寸 。

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  8. The scale of the map shows that 1 inch = 50 miles. If the map shows that there is 5 inches between the two cities, what is the actual distance?
     ::地图的大小显示 1 英寸 = 50 英里。 如果地图显示两个城市之间有 5 英寸, 实际距离是多少 ?
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  9. The scale of the map shows that 2 inches = 100 km. If the map shows that there are 3 inches between the two cities, what is the actual distance between them?
     ::地图的大小显示2英寸=100公里。 如果地图显示两个城市之间有3英寸,那么它们之间的实际距离是多少?
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  10. The scale of the map shows that 4 inches = 200 km. If the map shows that there are 5 inches between the two cities, what is the actual distance between them?
      ::地图的大小显示4英寸=200公里。如果地图显示两个城市之间有5英寸,它们之间的实际距离是多少?
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  11. The scale of the garden design shows that 2 inch = 3 feet. How big is the garden if the rectangular plot is 4″ × 6″?
      ::花园设计的规模显示2英寸=3英尺。如果长方形地块是 4 × 6,花园有多大?
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  12. The scale of the room design shows that 1 inch = 2 feet. How big is the actual room if the design shows a square that is 5 inches wide?
      ::房间设计的规模显示 1 英寸 = 2 英尺。 如果设计显示一个宽5 英寸的方形, 实际房间有多大 ?
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  13. The scale of the room design shows 2 inches = 4 feet. How big is the actual room if the design shows a square that is 10 inches wide?
      ::房间设计的规模为 2 英寸 = 4 英尺。 如果设计显示一个宽10 英寸的方形, 实际房间有多大 ?
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  14. Using this same scale, how big is the actual room if the design shows a square that is 15 inches wide?
      ::用同样的比例, 如果设计显示方形宽15英寸, 实际房间有多大?
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  15. Using this same scale, how tall is a building if the drawing is 12 inches tall?
      ::用同样的比例,如果图画高12英寸,那么大楼有多高?

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  Review (Answers) 
  ::回顾(答复)

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  Click   to see the answer key or go to the Table of Contents and click on the Answer Key under the 'Other Versions' option.
  ::单击可查看答题键, 或转到目录中, 单击“ 其他版本” 选项下的答题键 。

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  Resources
  ::资源