PQRS is a rhombus. If PR\(^2\) + QS\(^2\) = kPQ\(^2\), determine k.

  • A 1
  • B 2
  • C 3
  • D 4
jamb 1989mathematics

The correct answer is D. 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

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