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

January 29, 2021 | education

| **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.

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