Question

The area of rhombus is 2016 cm^2 and its sides are equal to 65 cm. Find the length of its diagonals.

Answer 1

For given rhombus ABCD; AB = 65 cm

let AO = x cm and BO = y cm (O is intersection point of diagonals AC and BD)

In ΔABO; AB²=AO²+BO²

implies x²+y²= 65² ...........1

Since area is 2016 cm²; 1/2 * 2x * 2y = 2016

implies xy =  1008 ............2

Using equations 1 and 2

(x+y)² = x²+y²+2xy = 65² + 1008*2 = 4225 + 2016 = 6241

x+y = 79

i.e x + $\frac{1008}{x}$  = 79

x² - 79x + 1008 = 0

implies x = 63 or 16

implies y =  16 or 63

Therefore lengths of diagonals (2*x and 2*y) are 126 cm and 32 cm