The perimeter of an isosceles triangle is 69 cm, find the sides, if the base is 12 cm larger.

1. Let one lateral side be equal to a cm, since it is isosceles, then the second is equal to a cm. From the condition, the base of the triangle is 12 cm larger than the lateral side and is equal to (a + 12) cm. The perimeter of an isosceles triangle is 69 cm , that is, the sum of all sides of the triangle. Let’s get and solve the equation:

a + a + (a + 12) = 69;

3a = 69 – 12;

3a = 57;

a = 69/3;

a = 19;

Consequently, the first and second lateral sides of an isosceles triangle are 19 cm each;

2. Find the length of the base of the triangle;

19 + 12 = 31 cm;

Answer: the sides are 19 cm, the base is 31 cm.