The perimeter of an isosceles triangle is four times the base and 10 cm more than the lateral side.

The perimeter of an isosceles triangle is four times the base and 10 cm more than the lateral side. Find the side of the triangle.

Let the base be x, the side be y, and P the perimeter. By the condition of the problem:

1) y + 10 = P,

2) 4 * x = P.

In addition, the perimeter is equal to the sum of the lengths of all sides:

3) x + 2 * y = P.

Subtract the first from the third equation, we get:

x + 2 * y – y – 10 = P – P;

x + y – 10 = 0;

x = 10 – y.

Substitute the resulting value for x into the second equation and equate it to the first:

4 * (10 – y) = y + 10;

40 – 4 * y = y + 10;

5 * y = 30;

y = 30/5 = 6 cm – the lateral side of this isosceles triangle.