Given an isosceles triangle P = 45 cm, one of the sides is 12 cm smaller than the other, find all sides.

Given:
triangle ABC – isosceles;
P avs = 45 centimeters;
Find the length of the sides of the triangle: AB, BC, CD -?
Solution:
1) Let AC be the base of the isosceles triangle ABC, and AB = BC – the sides.
2) Let’s say AC = x centimeters, then AB = BC = x + 12 centimeters. We know that P avs = 45 centimeters. Let’s make the equation:
x + x + 12 + x + 12 = 45;
x + x + x + 12 + 12 = 45;
3x + 24 = 45;
3x = 45 – 24;
3x = 21;
x = 21: 3;
x = 7 centimeters – the length of the AB side;
3) 7 + 12 = 19 centimeters – the lengths of the sides AB and BC.
Answer: 7 centimeters; 19 centimeters; 19 centimeters.