# The perimeter of an isosceles triangle is 112 cm, and its two sides are in a ratio of 2: 3. Find the sides of the triangle.

July 28, 2021 | education

| 1. A, B, C – the vertices of the triangle.

2. By the condition of the problem AB: AC = 2: 3. Therefore, AC = 3AB / 2.

3. Further calculations are performed using the formula for calculating the perimeter of a triangle:

AC + AB + BC = 112 centimeters.

BC = AB, since this triangle is isosceles.

4. Substitute AB instead of BC and 3AB / 2 instead of AC into the original formula:

3АВ / 2 + 2АВ = 112.

7AB / 2 = 112.

AB = 2 x 16 = 32 centimeters.

AC = 3 x 32: 2 = 48 centimeters.

Answer: AC = 48 centimeters, AB = BC = 32 centimeters.

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