In a △ABC, 'D' and 'E' are points on BC such that AD = AE and ∠BAD = ∠CAE. If AB = (2p + 3) units, BD = '2p' units, AC = (3q - 1) units and CE = 'q' units, then find the value of (p + q).
Show answer & explanation
Correct answer: D
Explanation
Given:
AD = AE
∠BAD = ∠CAE
AB = (2p + 3)
BD = 2p
AC = (3q − 1)
CE = q
AD = AE and ∠BAD = ∠CAE ⇒ ΔBAD ≅ ΔCAE
Hence,
AB = AC
BD = CE
2p + 3 = 3q − 1 ...(1)
2p = q ...(2)
Substituting (2) into (1),
2p + 3 = 3(2p) − 1
2p + 3 = 6p − 1
4 = 4p
p = 1
q = 2p = 2
p + q = 1 + 2 = 3