Find the length of the side of an isosceles triangle if its perimeter is 12cm larger than the base.

Let a standard isosceles triangle ABC be given.

AB = BC. Accordingly, the base of the triangle is the AC side.

The perimeter P of triangle ABC is the sum of the lengths of all its sides.

P = AB + BC + AC; Let’s transform:

P = 2 * AB + AC;

By the condition of the problem, P – AC = 12 cm; Then

2 * AB = P – AC;

2 * AB = 12;

AB = 6 cm.

Answer: The length of the lateral side of an isosceles triangle is 6 cm.