Question

If a side of rhombus is 4 CM then find the sum of the squares of its diagonals

Answer 1

Step-by-step explanation:

Suppose both diagonals are a & b

Diagonal of rhombus intersect each other equally and at 90° angle.

(a/2)² + (b/2)² = side²

a²/4 + b²/4 = 4²

(a² + b²) /4 = 16

a² + b² = 64

Now add 2ab on both side

a² + b² + 2ab = 64 + 2ab

(a + b) ² = 64 + 2ab

In the question value of (a+b) is given as 10.

(10)² = 64 + 2ab

2ab = 100 - 64 = 36

ab = 18

Area of rhombus = ab/2

Area = 18/2 = 9