Q. 194.0( 5 Votes )

In the given figure, ABCD is a trapezium whose diagonals AC and BD intersect at 0 such that OA = (3x —1) cm, OB = (2x + 1) cm, OC = (5x — 3) cm and OD = (6x — 5) cm. Then, x = ?


A. 2

B. 3

C. 2.5

D. 4

Answer :

ABCD is a Trapezium with AC and BD as diagonals and AB DC


In Δ AOB and Δ DOC


AOB = DOC (vertically opposite angles)


CDO = OBA (alternate interior angles) (AB DC and BD is transversal)


Δ AOB Δ DOC (AA similarity criterion)




=


18 x2 – 21x + 5 = 10 x2 – x – 3


8 x2 – 20 x + 8 = 0


2x2 – 5 x + 2 = 0


2x2 – 4 x – x + 2 = 0


2x (x- 2) – 1(x – 2) = 0


(2x- 1) (x -2) = 0


x = 1/2, 2


x = 1/2 is not possible so x = 2 cm

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