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

| February 17, 2021 | education

The triangle inequality says that the sum of the two sides of the triangle must be greater than the third side. Let’s denote the sides of the triangle as a, b and c, then:
a + b> c;
a + c> b;
b + c> a.
1. Let in an isosceles triangle the sides a and b are 5 cm, and the length of the base c is 11 cm then:
5 + 5> 11;
5 + 11> 5;
5 + 11> 5.
The first inequality does not hold, then an isosceles triangle with a side length of 5 cm and a base length of 11 cm does not exist.
2. Let in an isosceles triangle the sides a and b are 11 cm, and the length of the base c is 5 cm then:
11 + 11> 5;
11 + 5> 11;
11 + 5> 11.
All inequalities are satisfied, then an isosceles triangle with a side length of 11 cm and a base length of 5 cm exists.
Answer: base length 5 cm, side length 11 cm.



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