Question

In below figure, AB || CD. If OA = 3x – 19, OB = x – 4, OC = x – 3 and OD = 4, find x.

Answer 1

Since diagonals of a trapezium divide each other proportionally.

`therefore"AO"/"OC"="BO"/"OD"`

`rArr(3x-19)/(x-3)=(x-4)/4`

⇒ 4(3𝑥 − 19) = (𝑥 − 4)(𝑥 − 3)

⇒ 12x – 76 = x (x – 3) −4(x – 3)

⇒ 12𝑥 − 76 = 𝑥² − 3𝑥 − 4𝑥 + 12

⇒ 𝑥² − 7𝑥 − 12𝑥 + 12 + 76 = 0

⇒ 𝑥² − 19𝑥 + 88 = 0

⇒ 𝑥² − 11x − 8x + 88 = 0

⇒ 𝑥(𝑥 − 11) − 8(𝑥 − 11) = 0

⇒ (𝑥 − 11)(𝑥 − 8) = 0

⇒ 𝑥 − 11 = 0 or x – 8 = 0

⇒ x = 11 or x = 8