# Find the base and side of an isosceles triangle if its two sides are 5 cm and 11 cm.

August 27, 2021 | education

| It follows from the triangle inequality that the length of any side of a triangle is less than the sum of its two other sides.

Let a, b and c be the sides of the triangle, then:

a + b> c;

a + c> b;

b + c> a.

1. The sides of an isosceles triangle a and b are 5 cm each, and the base is 11 cm then:

5 + 5> 11;

5 + 11> 5;

5 + 11> 5.

Since 5 + 5 <11, then an isosceles triangle with a side equal to 5 cm and a base equal to 11 cm does not exist.

2. The sides of an isosceles triangle a and b are 11 cm each, and the base is 5 cm then:

11 + 11> 5;

11 + 5> 11;

11 + 5> 11.

All inequalities are satisfied, then an isosceles triangle with a side equal to 11 cm and a base equal to 5 cm exists.

Answer: base = 5 cm, side = 11 cm.

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