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If a rectangle has a perimeter of 20 and a diagonal

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by BTGmoderatorLU » Sun May 12, 2019 3:11 am

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Source: Magoosh

If a rectangle has a perimeter of 20 and a diagonal with length 9, what is the area of the rectangle?

A. 7.5
B. 8
C. 8.5
D. 9
E. 9.5

The OA is E
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by Scott@TargetTestPrep » Tue May 14, 2019 6:23 pm
BTGmoderatorLU wrote:Source: Magoosh

If a rectangle has a perimeter of 20 and a diagonal with length 9, what is the area of the rectangle?

A. 7.5
B. 8
C. 8.5
D. 9
E. 9.5

The OA is E
We can create the equations:

2W + 2L = 20

W + L = 10

And

L^2 + W^2 = 9^2

L^2 + W^2 = 81

Squaring the first equation we have:

W^2 + L^2 + 2LW = 100

Substituting we have:

81 + 2LW = 100

2LW = 19

LW = 9.5

Answer: E

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