The perimeter of an isosceles triangle is 180 cm, the base is 3 times the lateral side. Find sides.

The perimeter of a triangle is the sum of the lengths of its sides. Since, by the condition, an isosceles triangle is given, then its two sides are equal to each other, we denote them by x, and the base we denote by y.
Then it turns out:
x + x + y = 180;
2x + y = 180.
It is known from the condition that the base of the triangle is 3 times larger than its lateral side:
y = 3x
We get a system of linear equations:
2x + y = 180;
y = 3x.
Substitute the value of y from the second equation into the first:
2x + 3x = 180.
Let’s solve the resulting equation and find x – the length of the side:
5x = 180;
x = 180/5;
x = 36 cm – the length of the side.
Substitute the resulting value of x into the second equation of the system of linear equations and find the length of the base y:
y = 3x = 3 * 36 = 108 (cm)
Check: 36 + 36 + 108 = 180;
180 = 180.
Answer: the sides are 36 cm each, the base is 108 cm.