Question

PQRS is a rhombus whose diagonals are 16cm and 12cm . What is the length of its side ?

Answer 1

Answer:

One diagonal is 16 and another 12 then half of both is 8and6.diagonal of rhombus bisect at 90'

By pythogaurus theorem

8²+6²=h²

64+36=100

Side = 10

Answer 2

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

...