PQRS is a rhombus. If PR\(^2\) + QS\(^2\) = kPQ\(^2\), determine k.
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Correct Answer: Option D
Explanation:
PR\(^2\) + QS\(^2\) = kPQ\(^2\)
SQ\(^2\) = SR\(^2\) + RQ\(^2\)
PR\(^2\) + SQ\(^2\) = PQ\(^2\) + SR\(^2\) + 2RQ\(^2\)
= 2PQ\(^2\) + 2RQ\(^2\)
= 4PQ\(^2\)
∴ K = 4
PR\(^2\) + QS\(^2\) = kPQ\(^2\)
SQ\(^2\) = SR\(^2\) + RQ\(^2\)
PR\(^2\) + SQ\(^2\) = PQ\(^2\) + SR\(^2\) + 2RQ\(^2\)
= 2PQ\(^2\) + 2RQ\(^2\)
= 4PQ\(^2\)
∴ K = 4