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Question:

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

Explanation:

Let QS = x, we get the following figure

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In any triangle, the sum of any two sides must be greater than the third side. Similarly, the difference between any two sides must be smaller than the third side. Hence,

In ∆QRS,

x + 5 > 17

⇒ x > 12          …(i)

In ∆PQS,

x < 9 + 5

⇒ x < 14         …(ii)

Combining (i) and (ii), we get

12 < x < 14

Hence, option (b).