If the diagonal of a rectangle is 31 cm long and its perimeter is 78 cm. Find the area of rectangle in sq cm.

Answer 1

Let a and b be the sides of the rectangle.
Now 2*(a + b) = 78
(a + b) = 39.
a^2 + b^2 = 31^2
(a + b)^2 - 2ab = 961
39^2 - 961 = 2ab
(1521 - 961)/2 = ab = area of rectangle
Area of rectangle = 560/2 = 280 sq cm.