Let D and E be two points on the side BC of ΔABC such that AD = AE and ∠BAD = ∠EAC. If AB = (3x + 1) cm, BD = 9 cm, AC = 34 cm and EC = (y + 1) cm, then the value of 3(x+ y) is?
Answer & explanation
Correct answer: option 2
As AD = AE ⇒ ∠ ADE = ∠AED
In ΔADE
∠ ADE = ∠BAD + ∠ABD .....(1)
∠ AED = ∠EAC + ∠ACE .....(2)
On compare (1) and (2)
∠ABD = ∠ ACE
In ΔABC
∠B = ∠C
∴ AB = AC
⇒ 3x + 1 = 34 ⇒ x = 11
ΔABD ≅ ΔACE
∴ AB = AC and AD = AE
∠BAD = ∠EAC
∴ BD is also equal to EC
⇒ 9 = y + 1 ⇒ y = 8
3(x + y) = 3(11 + 8) = 3 × 19 = 57 cm