Question

8. The lengths of the diagonals of a rhombus are 16 cm and 12 cm. Find the side of the rhombus,​

Answer 1

Given : ABCD  is a rhombus .

AC and BD are the diagonals .

AC = 16 cm , BD = 12 cm

Proof :

We know that , diagonals in a rhombus   bisect each other

perpendicularly.

Let O is the intersecting point of diagonals AC and BD.

OA = AC/2 = 16/2 = 8 cm

OB = BD/2 = 12/2 = 6 cm

Now ,

IN Δ AOB , ∠AOB = 90°

By Pythagorean Theorem ,

AB² = OA² + OB²

⇒ AB² = 8² + 6²

        = 64 + 36

        = 100

∴ AB = √100 = 10 cm

Perimeter of the Rhombus = 4 × side

P = 4 × AB

P = 4 × 10 = 40 cm

...

I have found both side and Perimeter of the Rhombus.