The perimeter of an isosceles triangle is 50 cm, and one of its sides is 13 cm smaller

The perimeter of an isosceles triangle is 50 cm, and one of its sides is 13 cm smaller than the other. Find the sides of the triangle.

a – the base of the triangle;

b = c – lateral sides of the triangle;

P = a + b + c = a + 2 b;

1). a = b + 13;

P = b + 13 + 2 b; 3 b = P – 13 = 50 – 13 = 37 (cm);

b = c = 12 1/3 cm; a = 25 1/3 cm;

This triangle does not exist, since a + b <c;

2). a = b – 13;

P = b – 13 + 2 b; 3 b = P + 13 = 50 + 13 = 63 (cm);

b = c = 21 cm; a = 8 cm.