XAT 2014 Question 54

Question 54

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

Solution

In a triangle , sum of two sides is greater than the third side and difference of two sides is less than third side.

In $$\triangle$$ PQS

=> $$QS < 9 + 5$$ => $$QS < 14$$ ------Eqn(I)

In $$\triangle$$ QRS

=> $$QS > 17 - 5$$ => $$QS > 12$$ ------Eqn(II)

From eqn(I) & (II)

=> $$12 < QS < 14$$



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