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

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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

Junior | Next Rank: 30 Posts
Posts: 24
Joined: 29 Jun 2011
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.