Question

In the given figure, ABCD is a trapezium whose diagonals AC and BD intersect at O 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 1

(a) 2 

We know that the diagonals of a trapezium are proportional.

Therefore

OA/OC = OB/OD 

⇒ 3x−1/5x−3 = 2x+1/6x−5 

⇒ (3X – 1) (6X – 5) = (2X + 1) (5X -3)

when x = 1/2 , 6x − 5 = −2 < 0, which is not possible. 

Therefore, x = 2