Let D and E be two points on the side BC of △ABC 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 (x + y) is:
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 19.
In △ABD and △AEC,
∠BAD = ∠EAC , AD = AE and ∠AED = ∠ADE.
So one can say that,
△ABD and △AEC are similar.
BD/EC = AB/AC = AD/AE = 1/1
9/(y + 1) = (3x + 1)/34 = 1/1
On comparing we get,
y = 8 and x = 11
x + y = 11 + 8 = 19.