2.6未知维度使用公式

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  未知维度使用公式

  
  

  

  [Figure 1]

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  Anna wants to redecorate an old table. She wants to put decorative tape around the outside of the table. The problem is, she only knows the  area  of the table and one side length. She needs to know the other side length in order to get enough tape to cover all four sides. The area of the table is 32  square  feet and the length of the table is 8 feet. Anna needs to solve for the missing dimension to determine if a roll of tape that is 25 feet long will be enough tape.
  ::Anna想重新装修一张旧桌子。 她想把装饰性胶带放在桌子的外面。 问题是, 她只知道桌子的面积和一面长度。 她需要了解另一侧长度, 才能得到足够覆盖四面的磁带。 桌子的面积是32平方英尺, 桌子的长度是8英尺。 Anna需要解决缺失的维度, 才能确定一卷25英尺长的胶带是否足够。

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  In this concept, you will learn how to figure out unknown  dimensions  of length or width when given the area or  perimeter  of a figure.
  ::在这个概念中,如果给出一个图的面积或周界,您将学会如何找出未知的长度或宽度尺寸。

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  Unknown Dimensions
  ::未知尺寸

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  Dimensions  are measurements needed in order to find the area or perimeter of a square or  rectangle . The dimensions that you are familiar with are length and width (or side length in a square). Sometimes, a math problem presents missing dimensions but provides the area or perimeter to help you solve the missing dimension.
  ::尺寸是找到一个正方形或矩形的面积或周边所需的测量。 您熟悉的尺寸是长度和宽度( 或方形的侧长 ) 。 有时数学问题呈现缺失的维度, 但提供区域或周边帮助您解决缺失的维度 。

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  For example, there is a square with a perimeter of 12 inches. Find the side length of the square.
  ::例如,有一个面积12英寸的广场,找到广场的侧长。

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  First, write the formula for the perimeter of a square.
  ::首先,写出广场周边的公式。

  $$\begin{array}{r}P=4s\end{array}$$

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  Next, fill in the known information. This problem provides the perimeter or  $\begin{array}{r}P\end{array}$ . Plug that information into the formula.
  ::接下来填入已知信息。 这个问题提供周边或 P. 。 将这些信息插入公式中 。

  $$\begin{array}{r}12=4s\end{array}$$

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  Then, to solve the equation, you can either rewrite the equation to make it a division problem, or ask yourself what number multiplied by 4 gives you a total of 12. Either strategy will get you the answer of 3.
  ::然后,为了解答方程式,你要么改写方程式,使它成为一个分裂问题, 要么问问你自己,如果数字乘以4,你就会得到12, 任何一种策略都会得到3的答案。

  $$\begin{array}{rl}12÷4& =s\\ 3& =s\\ & or\\ 12& =4(3)\\ 12& =12\end{array}$$

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  Sometimes a figure is presented and the area of that figure is provided.
  ::有时提出一个数字,并提供数字所涉领域。

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  For example, find the side length for a square with an area of 36 sq. in.
  ::例如,找到一个面积为36平方米的方形的侧长。

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  First, use the formula for finding the area of a square.
  ::首先,使用公式来找到一个方形的区域。

  $$\begin{array}{rl}A& =s\times s\\ 36& =s\times s\end{array}$$

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  Then, think, “What number times itself will give me 36?” The answer is 6. 
  ::那么,你想想,“给我36次多少次?” 答案是6次。

  $$\begin{array}{rl}36& =6\times 6\\ 36& =36\end{array}$$

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  Double check your work by making sure the answer multiplied by itself gives the area. In this case, the answer checks out as 6 times 6 does equal 36.
  ::双倍检查您的工作, 确定答案乘以本身给定区域。 在此情况下, 答案为 6 乘以 6 等于 36 。

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  This same concept works for  , only you use the formula that is more appropriate for rectangles. 
  ::此概念同样有效, 只有您使用适合矩形的公式 。

  $$\begin{array}{rl}P& =2(l)+2(w)\\ A& =l\cdot w\end{array}$$

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  When the perimeter or area is given, you plug in the information given and solve for the missing dimension. The concept for area works the same as for a square only length and width are used instead of "s" for side length. When solving for a missing dimension when the perimeter is given in a rectangle, it looks a little different than with a square.
  ::当给定周边或区域时,您将插入给定的信息,并解决缺失的维度。区域的概念与仅用正方形的长度相同,使用宽度,而不是侧长的“s”。当在矩形中给定周边时解决缺失的维度时,它看起来与方形略有不同。

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  For example, find the width of a rectangle whose perimeter is 18 inches and the length is 6 inches.
  ::例如,找到圆周18英寸、长6英寸的矩形宽度。

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  First, write the formula and substitute the given information.
  ::首先,写入公式并替换给定信息。

  $$\begin{array}{r}18=2(6)+2(w)\end{array}$$

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  This equation shows that the only variable present is the width, the missing dimension. Solve what can be solved first in the problem before isolating the variable "w".
  ::此方程式显示, 当前唯一的变量是宽度, 缺少的维度。 在分隔变量“ w” 之前先解决问题中可以先解决的问题 。

  $$\begin{array}{r}18=12+2w\end{array}$$

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  Then, to isolate the 2w, subtract the 12 from both sides of the equation. That leaves the equation looking like this:
  ::然后,为了分离 2w, 从方程的两侧减去 12。 这样方程就像这样了:

  $$\begin{array}{r}6=2w\end{array}$$

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  Now either rewrite the equation as division or ask yourself what number times 2 gives you 6. 
  ::现在要么将方程式重写为“除法”,要么问问自己,数字乘以2给了你6

  $$\begin{array}{rl}6÷2& =w\\ 3& =w\\ & or\\ 6& =2(3)\end{array}$$

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   The missing width is 3 inches.
  ::缺失的宽度为3英寸。

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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 Anna and her table.
  ::早些时候,你得到一个问题 关于安娜和她的桌子。

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  She knows the area of the table is 32 sq. ft. and the length is 8 feet. She needs to find the width of the table to then determine if 25 ft. of tape is enough.
  ::她知道桌子的面积是32平方英尺,长度是8英尺。她需要找到桌子的宽度,然后确定磁带的25平方英尺是否足够。

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  First, Anna writes out the formula to solve for the missing dimension. 
  ::首先,安娜写出解决缺失维度的公式

  $$\begin{array}{r}A=l\cdot w\end{array}$$

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  Next, Anna plugs in the information she has already. She knows the area and the length.
  ::接下来,安娜在她已经掌握的信息中插了插座 她知道那个区域和长度

  $$\begin{array}{r}32=8\cdot w\end{array}$$

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  Then, she solves for the missing dimensions (width) by dividing 32 by 8.
  ::然后,她通过将32除以8 来解决缺失的维度(宽)问题。

  $$\begin{array}{rl}32÷8& =w\\ 4& =w\end{array}$$

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  The missing width is 4 feet. But now, Anna needs to figure out if she has enough tape. Now that Anna knows both dimensions of the table, she can figure out the perimeter of the outside of the table by using the formula.
  ::缺少的宽度是四英尺。 但是现在,安娜需要弄清楚她是否有足够的磁带。 现在安娜知道桌子的两维尺寸了, 她可以通过使用公式来弄清楚桌子外面的周边。

  $$\begin{array}{rl}P& =2(8)+2(4)\\ P& =16+8\\ P& =24\end{array}$$

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  The total perimeter of Anna's table is 24 feet, which means 25 feet of tape is enough.
  ::安娜桌子的四周是24英尺 这意味着25英尺的胶带就足够了

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  Example 2
  ::例2

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  A square garden has an area of 144 square meters. What is the side length of the plot?
  ::广场花园面积为144平方米。这块地的侧长是多少?

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  First, write the formula for area of a square.
  ::首先,写一个正方形区域的公式。

  $$\begin{array}{r}A=s\cdot s\end{array}$$

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  Next, plug in the information given in the problem. The area is given so that substitutes for A
  ::下一步, 插入在问题中给出的信息。 给此区域指定 A 的替代品

  $$\begin{array}{r}144=s\cdot s\end{array}$$

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  Then, figure out which number times itself will gives you 144. The answer is 12.
  ::然后,想清楚自己会给你多少次数144 答案是12次

  $$\begin{array}{r}144=12\times 12\end{array}$$

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  The answer is 12 feet.
  ::答案是12英尺

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  Example 3
  ::例3

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  Find the side length of a rectangle that has a perimeter of 48 feet and a width of 9 feet.
  ::找到一个长长的矩形的侧长48英尺,宽度9英尺。

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  First, write out the formula for perimeter of a rectangle.
  ::首先,写出矩形周边的公式。

  $$\begin{array}{r}P=2(l)+2(w)\end{array}$$

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  Next, plug in the given information. Solve that parts of the equation that can be solved already.
  ::下一步, 插入给定的信息 。 解决方程式中已经可以解答的部分 。

  $$\begin{array}{rl}48& =2(l)+2(9)\\ 48& =2(l)+18\end{array}$$

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  Then, isolate the missing dimension variable and solve for the final answer.
  ::然后分离缺失的维度变量, 并解决最终答案 。

  $$\begin{array}{rl}30& =2(l)\\ 30÷2& =l\\ 15& =l\end{array}$$

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  The answer is 15 feet.
  ::答案是15英尺

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  Example 4
  ::例4

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  Find the side length of a square that has a perimeter of 56 feet.
  ::找到方形的侧长56英尺

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  First, write the formula for perimeter of a square.
  ::首先,写出广场周边的公式。

  $$\begin{array}{r}A=4(s)\end{array}$$

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  Next, plug in the given information.
  ::下一步,插入给定的信息。

  $$\begin{array}{r}56=4(s)\end{array}$$

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  Then, solve for the side length.
  ::然后,解决侧长。

  $$\begin{array}{rl}56÷4& =s\\ 14& =s\end{array}$$

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  The answer is 14 feet.
  ::答案是14英尺

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  Example 5
  ::例5

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  Find the side length of a rectangle that has an area of 120 sq. miles and a length of 12 miles.
  ::找到一个矩形的侧长 其面积为120平方英里 长度为12英里

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  First, write the formula for area of a rectangle.
  ::首先,写一个矩形区域的公式。

  $$\begin{array}{r}A=l\cdot w\end{array}$$

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  Next, plug in the given information.
  ::下一步,插入给定的信息。

  $$\begin{array}{r}120=12\cdot w\end{array}$$

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  Then, solve for the missing dimension.
  ::那么,解决缺失的维度。

  $$\begin{array}{rl}120÷12& =w\\ 10& =w\end{array}$$

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  The answer is 10 feet.
  ::答案是10英尺

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  Review
  ::回顾

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  Find the side length of each square given its perimeter.
  ::找到每个广场的侧长 以其周界。

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  1. P = 24 inches
     ::P=24英寸
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  2. P = 36 inches
     ::P=36英寸
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  3. P = 50 inches
     ::P=50英寸
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  4. P = 88 centimeters
     ::P=88厘米
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  5. P = 90 meters
     ::P=90米
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  6. P = 20 feet
     ::P=20英尺
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  7. P = 32 meters
     ::P=32米
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  8. P = 48 feet
     ::P=48英尺

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  Find the side length of each square given its area.
  ::根据面积查找每个广场的侧长。

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  9. A = 64 sq. inches
     ::A=64平方英寸
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  10. A = 49 sq. inches
      ::A=49平方英寸
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  11. A = 121 sq. feet
      ::A=121平方英尺
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  12. A = 144 sq. meters
      ::A=144平米
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  13. A = 169 sq. miles
      ::A=169平方英里
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  14. A = 25 sq. meters
      ::A=25平方米
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  15. A = 81 sq. feet
      ::A=81平方英尺
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  16. A = 100 sq. miles
      ::A=100平方英里

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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