# The half-perimeter of an isosceles triangle is 15, and the base relative to the side is 3: 2. find the base.

September 12, 2021 | education

| Let the side of a given isosceles triangle be a, half the base equal to b. The half-perimeter of an isosceles triangle is equal to the sum of the lengths of the lateral side and half of the base:

a + b = 15;

a = 15 – b.

The base refers to the side as 3/2, which means:

2b / a = 3/2.

Hence:

4b = 3a = 3 * (15 – b) = 45 – 3b;

7b = 45;

b = 45/7;

2b = 90/7 ≈ 12.86 – the required base.

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