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

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

by AAPL » Fri Sep 25, 2020 2:47 pm

00:00

A

B

C

D

E

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Magoosh

If a rectangle has 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

OA E

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

by psarma » Sat Sep 26, 2020 11:53 am
Let l be the length and b the breadth
Perimeter is 20
So, 2(l+b)=20
i.e l+b=10
Squaring both sides,
$$^{l^2}$$ + $$^{b^2}$$ + 2lb = 100

Also, diagonal is 9,
So, $$^{l^2}$$ + $$^{b^2}$$ = $$^{9^2}$$
Or $$^{l^2}$$ + $$^{b^2}$$ = 81

Subtracting 2nd equation from 1st,
we get 2lb = 19
or lb = 9.5

Area = lb = 9.5
Option E.

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