Question

PQRS is a rhombus with RQ = 10cm and the diagonal PR = 12 cm. Find the length of QS

correct ans = 16 cm.

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Answer 1

Answer:

PR=12cm (given)

⇒1/2PR= 1/2 *12

⇒OR= 6 cm (Diagonals bisect each other)

ΔOQR is a right angled triangle as diagonals bisect each other at 90°.

Acc to Pythagoras thm,

OQ²+OR²=QR²

OQ²+6²=10²

OQ²+36=100

OQ²=100-36=64

OQ=√64

OQ=8 CM

Since diagonals bisect each other,

OQ=OS=8 CM

QS= OQ+OS=8+8=16 CM

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Answer 2

Answer:

in ∆ROQ

<ROQ=90°

so RQ= hypotenuse

so RQ²= RO² + OQ²

so 10²= 6²+ OQ²(PR =12 , RO=6)

so OQ²= 100-36=64

so OQ=8

so QS = 8×2=16

thank you