In the given figure, ABCD is trapezium whow diagonals AC and BD inters – InterviewSolution

InterviewSolution

1.	In the given figure, ABCD is trapezium whow 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=?
Answer» Correct Answer - A We know that the diagonals of trapezium divide each other proportionally. `:. (OA)/(OC)=(OB)/(OD)rArr (3x-1)/(5x-3)=(2x-1)/(6x-5)` `rArr (3x-1)(6x-5)=(5x-3)(2x+1)` `rArr 18x^(2)-21x+5=10x^(2)-x-3 rArr 8x^(2)-20x+8=0` `rArr 2x^(2)-5x+2=0 rArr 2x^(2)-4x+2=0 rArr 2x(x-2)-(x-2)=0` `rArr (x-2)(2x-1)=0 rArr x=2 or x =(1)/(2)` But, `x=(1)/(2)` gives (`6x-5) lt 0` and the distance cannot be negative . `:. x=2`

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