# In an isosceles triangle, the lateral side relates to the base 2: 3. find the sides of the triangle if its perimeter is 28 cm.

Since the triangle is isosceles, its hips are the same.

Due to the fact that the ratio of the sides of the triangle is indicated in the condition, we should determine the value of one unknown x.

To solve the problem, let’s compose an alphabetic expression in which:

P is the perimeter of an isosceles triangle;

2 * x – the size of the hip of the triangle;

3 * x – the size of the base of the triangle.

The perimeter is the sum of the sides of the triangle, so we get the following equation:

P = 2 * x + 2 * x + 3 * x.

P = 7 * x.

Substitute the known data instead of the P value.

28 = 7 * x.

x = 28/7 = 4 cm.

In this case, the base of the triangle will be:

3 * x = 4 * 3 = 12 cm.

The sides of the triangle will be equal:

2 * x = 2 * 4 = 8 cm.

Answer:

12, 8 and 8 cm.

Solving a similar problem arithmetically

The task:

The perimeter of an isosceles triangle is 45 cm. Find its sides if its lateral side is 2: 5 to the base.

The solution of the problem:

First, you should determine the total number of parts in relation.

Since the sides of the triangle are equal to each other, we get:

2 + 2 + 5 = 9 pieces.

We find the size of the base.

Since it is 5 parts, we get:

45 * 5/9 = 225/9 = 25 cm.

We find the value of the side:

45 * 2/9 = 90/9 = 10 cm.

Answer: 10, 10 and 25 cm.