Question

In the given figure, PQRS is a trapezium, such that PQ || SR. Find x.

Answer 1

4/5 = x/(2x + 4)

9(2x + 4) = 5 (x + 5)

8x + 16 = 5x + 25

8x - 5x = 25 - 16

3x = 9

x = 3

Answer 2

Complete Question :- In the given figure (Refer to image) , PQRS is a trapezium, such that PQ || SR. Find x ?

a) 2 b) 5 c) 3 d) 4

Solution :-

In ∆POQ and ∆ROS we have,

→ ∠OPQ = ∠ORS { since PQ || SR , alternate interior angles }

→ ∠OQP = ∠OSR { since PQ || SR , alternate interior angles }

so,

→ ∆POQ ~ ∆ROS { By AA similarity }

then,

→ OQ/OS = PO/RO { when two ∆'s are similar their corresponding sides are in same ratio }

putting given values from we image we get,

→ (x + 5)/(2x + 4) = 4/5

cross - multiply,

→ 5(x + 5) = 4(2x + 4)

→ 5x + 25 = 8x + 16

→ 8x - 5x = 25 - 16

→ 3x = 9

dividing both sides by 3,

→ x = 3 (Ans.)

Hence, value of x is equal to option (c) 3 .

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