Question

PQRS is a rhombus whose diagonals PR and QS interect at O if PQ is 10 cm and diagonal QS is 16 cm, find the length of diognal PR

Answer 1

Hope this helps you.

Answer 2

Answer:

Diagonal PR = 12cm.

Step-by-step explanation:

PQRS is a rhombus

All sides in a rhombus are equal

Diagonals of a rhombus bisect each other at 90°

PQ = 10cm

QS = 16cm

QO +OS = 16c

QO = 8cm

OS = 8cm

In ΔPOS,

(PS)² = (PO)² + (SO)²  (∵ by Pythagoras theorem)

(10)² = (PO)² + (8)²

(PO)² = 100 - 64

(PO)² = 36

PO = 6

So, PR = 2 × PO

PR = 2 × 16 = 12cm

Therefore, diagonal PR = 12cm.