SOLUTION: the perimeter of a rectangle is 18 cm.its length is 7cm.if the ratio of the length to the width remains the same what is the area of the resulting rectangle when the perimeter of

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Question 1011812: the perimeter of a rectangle is 18 cm.its length is 7cm.if the ratio of the length to the width remains the same what is the area of the resulting rectangle when the perimeter of the original triangle is tripled?
Found 2 solutions by ikleyn, MathTherapy:
Answer by ikleyn(52810)   (Show Source): You can put this solution on YOUR website!
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the perimeter of a rectangle is 18 cm.its length is 7cm.if the ratio of the length to the width remains the same what is the area of the resulting rectangle when the perimeter of the original triangle is tripled?
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(18*3)*(7*3) = . . . ?


Answer by MathTherapy(10555)   (Show Source): You can put this solution on YOUR website!
the perimeter of a rectangle is 18 cm.its length is 7cm.if the ratio of the length to the width remains the same what is the area of the resulting rectangle when the perimeter of the original triangle is tripled?
Perimeter: 18 cm

Length: 7 cm



Let width be W. Then we get:

2(L + W) = 18

2(7 + W) = 18

14 + 2W = 18

2W = 18 – 14

2W = 4

W, or width = , or 2 cm



Ratio of length to width = 7:2



Tripling the original rectangle’s perimeter makes the new rectangle’s perimeter: 3(18), or 54 cm  

New rectangle’s length-to-width ratio = 7:2 (same as old), and perimeter = 54 cm

We then get: 

With x being the multiplicative factor, new rectangle’s length = 7x, and its width = 2x

We then get: 2(7x + 2x) = 54

2(9x) = 54

18x = 54

x = , or 3



Therefore, 

Length of new rectangle = 7(3), or 21 cm

Width of new rectangle = 2(3), or 6 cm

Area of new rectangle: 21(6), or  

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