SOLUTION: draw and label a rectangle that has a perimeter of 60 cm and an area of 200 square centimeters

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Question 674411: draw and label a rectangle that has a perimeter of 60 cm and an area of 200 square centimeters
Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
draw and label a rectangle that has a perimeter of 60 cm and an area of 200 square centimeters
       Perimeter = 2×Length + 2×Width
            Area = Length×Width

              60 = 2L + 2W
             200 = LW

Splve the first equation for W and substitute in the second equation:

              60 = 2L + 2W

Divide through by 2

              30 =  L +  W

          30 - L = w 


Substitute (30 - L) for W in

             200 = LW

             200 = L(30 - L)

             200 = 30L - L²

Get 0 on the right:

  L² - 30L + 200 = 0

Factor the left side:

(L - 20)(L - 10) = 0

Use the zero-factor property:

  L - 20 = 0;   L - 10 = 0
       L = 20;       L = 10

Subdtitute in

  30 - L = w    30 - L = w    
 30 - 20 = W   30 - 10 = W 
      10 = W        20 = W

We usually think of the length as the longer side, so

the length is 20 and the width is 10


Width = 10 centimeters
                  Length = 20 centimeters

Edwin
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