Question

Given: ∆ABC, AB = BC, m∠1<90°. Perimeter of ∆ABC = 25. Difference between two sides is 4. Find: AB, BC, AC. Can someone help me !!!!

Answer 1

AB = 7, BC = 7 and AC = 11

Explanation:

Let AB = BC = a and CA = b

Now, given that the perimeter of the triangle is 25.

So, 2a + b = 25 ............ (1)

And 4 is the difference between the two unequal sides.

Hence, b - a = 4 .............. (2)

⇒ 2b - 2a = 8 ........... (3)

Now, solving equations (1) and (3) we get, 3b = 25 + 8 = 33

⇒ b = 11

Hence, from equation (2) we get a = b - 4 = 7

Therefore, AB = 7, BC = 7 and AC = 11 (Answer)