Question

In triangle ABC, D is a point on BC such that ΔABD and ΔACD are congruent. Find the values of x and y, if AB = 2x + 3, AC = 3y + 1, BD = x and DC = y + 1.

Answer 1

From the adjacent figure ΔABC, D is a point on BC.

Such that ΔABD ≅ ΔACD

AB = 2x + 3 

AC = 3y + 1 

BD = x 

DC = Y + 1 

Δ ABD = Δ ACD 

⇒ AB = AC 

⇒ 2x + 3 = 3y + 1 

⇒ 2x – 3y + 2 = 0 …………….(1) 

BD = CD 

⇒ x = y + 1 

⇒ x – y – 1 = 0 ………………….(2)

⇒ from (1) & (2)

y = 4 

from (2) ⇒ x – 4 = 1 

⇒ x = 1 + 4 = 5

∴ (x, y) = (5, 4)