# 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. 2B. 3C. 2.5D. 4

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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