In the figure below, AB ∥ CD. Find the value of x.
Explanation:
Given, AB || CD.
Consider ∆AOB and ∆COD
∠AOB = ∠COD (Vertically opposite angles) and
∠ABD = ∠CDB (alternate interior angles)
∴ ∆AOB ~ ∆COD
⇒ AO/CO = BO/DO
⇒ 4/(4x - 4) = (2x - 1)/(2x + 4)
⇒ 1/(x - 1) = (2x - 1)/(2x + 4)
⇒ 2x + 4 = 2x2 - 3x + 1
⇒ 2x2 – 5x – 3 = 0
⇒ (2x + 1)(x - 3) = 0
⇒ x = -1/2 or 3
Since x has to be positive, x = 3
Hence, option (b).
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