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

September 26, 2021 | education

| **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.

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