If the diagonal of a rectangle is 12cm long and its perimeter is 28 cm. Find the area of the rectang

M4maths Previous Puzzles

13 Nov 2019 Area

If the diagonal of a rectangle is 12cm long and its perimeter is 28 cm. Find the area of the rectangle.

OPtion

1) 28
2) 22
3) 20
4) 16
5) 21
6) 23
7) 24
8) 26
9) 32
10) None of these

Solution

Let the sides of a rectangle be x & y cm, then
Diagonal² = x² + y²
144 = x² + y² ---(i)
Also, Perimeter = 2(x+y) = 28 => (x+y) = 14 ---(ii)
We know, (x+y)² = x² + y² + 2xy
=> 14² = 144 + 2xy
Solving we get
xy = 26

Correct Option: 8 Best Solution (2)