Question

In the given figure, ABCD is a trapezium in which AB || DC and its diagonals intersect at O. If AO = (5x – 7), OC = (2x + 1), BO = (7x – 5) and OD = (7x + 1), find the value of x.  

 

In the adjoining figure, ABCD is a trapezium in which CD || AB and its diagonals intersect at O. If AO = (2x + 1) cm, OC = (5x – 7) cm, DO = (7x – 5) cm and OB = (7x + 1) cm, find the value of x.

Answer 1

In trapezium ABCD, AB ‖ CD and the diagonals AC and BD intersect at O. Therefore,  

`(AO)/(OC)=(BO)/(OD)` 

⇒ `(5x-7)/(2x+1)=(7x-5)/(7x+1)`  

⟹ (5x-7) (7x+1) = (7x-5) (2x+1) 

⟹`35x^2+5x-49x-7=14x^2-10x+7x-5`
⟹ `21x^2-41x-2=0` 

⟹`21x^2-42x+x-2=0` 

⟹`21x(x-2)+1(x-2)=0` 

⟹`(x-2) (2x+1)=0` 

⟹ `x=2,1/21` 

∵ `x ≠-1/21` 

∴ x=2