In the given figure, ABCD is a trapezium in which AB║DC and its diag

1.	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.
Answer» 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) ⇒35x² + 5x – 49x – 7 = 14² – 10x + 7x – 5 ⇒ 21x² – 41x – 2 = 0 ⇒ 21x²– 42x + x -2 =0 ⇒ 21x (x-2) +1 (x-2) =0 ⇒ (x-2) (21x + 1) =0 ⇒ x = 2, - 1/21 ∵ x ≠ - 1/21 ∴ x = 2

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.

Answer»

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)

⇒35x² + 5x – 49x – 7 = 14² – 10x + 7x – 5

⇒ 21x² – 41x – 2 = 0

⇒ 21x²– 42x + x -2 =0

⇒ 21x (x-2) +1 (x-2) =0

⇒ (x-2) (21x + 1) =0

⇒ x = 2, - 1/21

∵ x ≠ - 1/21

∴ x = 2