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 = ?
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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