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  • ABCD is a trapezium whose diagonals AC and BD intersect at O such that OA = (3x - 1) m, OB = (2x + 1) m, OC = (5x -3) m and OD = (6x -3) m. Then, x = ?Option: 1<

ABCD is a trapezium whose diagonals AC and BD intersect at O such that OA = (3x - 1) m, OB = (2x + 1) m, OC = (5x -3) m and OD = (6x -3) m. Then, x = ?

Option: 1

2 m


Option: 2

0.5 m


Option: 3

Both (a) and (b)


Option: 4

None of the above


Answers (1)

best_answer

The diagonals of a trapezium divide each other proportionally

\\\therefore \quad \frac{O A}{O C}=\frac{O B}{O D} \Rightarrow \frac{3 x-1}{5 x-3}=\frac{2 x+1}{6 x-5} \\\\\Rightarrow \quad(3 x-1)(6 x-5)=(5 x-3)(2 x+1) \\\Rightarrow 18 x^{2}-21 x+5=10 x^{2}-x-3 \Rightarrow 8 x^{2}-20 x+8=0 \\\Rightarrow \quad 2 x^{2}-5 x+2=0 \Rightarrow 2 x^{2}-4 x-x+2=0 \Rightarrow 2 x(x-2)-(x-2)=0 \\\Rightarrow \quad(x-2)(2 x-1)=0 \Rightarrow x=2\text{ or }x=\frac{1}{2} \\\text{But, } x=\frac{1}{2}\text{ gives }(6 x-5)<0\text{ and the distance cannot be negative.} \\\therefore \quad x=2

Posted by

himanshu.meshram

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