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Diagonal Length in Quadrilateral

XAT 2014 · Quantitative Ability & Data Interpretation · Medium · Geometry

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In quadrilateral PQRS, PQ = 5 units, QR = 17 units, RS = 5 units, and PS = 9 units. The length of the diagonal QS can be:

  1. A.

    10 and < 12

  2. B.

    12 and < 14

  3. C.

    14 and < 16

  4. D.

    16 and < 18

  5. E.

    cannot be determined

Answer

B

Explanation

In △PQS\triangle PQS: ∣PS−PQ∣<QS<PS+PQ  ⟹  4<QS<14|PS - PQ| < QS < PS + PQ \implies 4 < QS < 14. In △QRS\triangle QRS: ∣QR−RS∣<QS<QR+RS  ⟹  12<QS<22|QR - RS| < QS < QR + RS \implies 12 < QS < 22. Combining both inequalities: 12<QS<1412 < QS < 14.

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