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
If a rectangle has perimeter of 20 and a diagonal with length 9, what is the area of the rectangle?
This topic has expert replies
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.
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.