# How to find the perimeter of an isosceles triangle if one side is 2.5 and the other is 3 times larger?

Suppose we are considering triangle ABC. According to the terms of the assignment, triangle ABC is isosceles. Let’s say that AB = BC. Then the lengths of the sides AB = BC cannot be equal to 2.5. Otherwise, the length of the third side will be greater than the sum of the lengths of the two sides, which is impossible for any triangle.

Let’s say AC = 2.5. Then, at the request of the task, we will compose the following proportion: AC: AB = 1: 3. Substitute the known value of AC in its place and solve the proportion: 2.5: AB = 1: 3. According to the basic property of the proportion, 1 * AB = 3 * 2.5, that is, AB = 7.5. Then BC = AC = 7.5.

We calculate the perimeter P of this triangle by summing the lengths of all sides of the triangle: P = AB + BC + AC = 7.5 + 7.5 + 2.5 = 17.5.

Answer: 7.5.