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?

57 cm

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