The perimeter of an isosceles triangle = 15 cm, and one of its sides is 4 cm less than the other. Find the sum of the sides.

We know that a triangle is isosceles, which means that, according to the definition, its lateral sides are equal to each other.

There are two solutions.

First option.

Let’s denote by x – the side, then x – 4 – the base.

We get the equation:

P = 2a + b;

2x + x – 4 = 15;

3x = 19;

x = 6 1/3 – side, then 6 1/3 + 6 1/3 = 12 2/3 cm the sum of the sides.

Second option.

Let x cm – the base of the triangle, the lateral side – (x – 4) cm.We get the equation:

x + 2 (x – 4) = 15;

x + 2x – 8 = 15;

3x = 23;

x = 7 2/3 cm base.

7 2/3 – 4 = 3 2/3 cm – side.

The sum of the sides: 3 2/3 + 3 2/3 = 7 1/3 cm (does not satisfy the triangle inequality theorem).

Answer: 12 2/3 cm.