In a triangle ABC, DE is parallel to BC and AD = a, DB = a + 4, AE = 2a + 3, EC = 7a. What is the value of 'a' if a > 0?
Show answer & explanation
Correct answer: B
Explanation
The correct answer is option 2 i.e 3
The triangle ∆ABC & ∆ADE are similar by AA similarity
⇒ AD/AB = AE/AC
⇒ a/(a + a + 4) = (2a + 3)/(2a + 3 + 7a)
⇒ a/(2a + 4) = (2a + 3)/(9a + 3)
⇒ a(9a + 3) = (2a + 3)(2a + 4)
⇒ 5a2 - 11a - 12 = 0
By solving the above quadratic equation:
⇒ (5a + 4)(a - 3) = 0
⇒ a = 3 (∴ a > 0)