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Question

PQRS is a rhombus with PQR=54. Determine PRS
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A
PRS=53
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B
PRS=63
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C
PRS=73
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D
PRS=83
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Solution

The correct option is C PRS=63
Given that PQRS is a rhombus

PSR=PQR=54 (opp. S of a rhombus are equal)

OSR=12×PSR=12×54=27 (SQ bisects PSR)

Now in ΔOSR

ORS+ROS+OSR=180

ORS+27+90=180

(Diagonals of a rhombus bisect each other at right s)

ORS=63

PRS=63

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