One side of an isosceles triangle is 4 cm, find the other two sides if the perimeter of the triangle is 14 cm

| February 27, 2021 | education

We write the formula for the perimeter of an isosceles triangle
P = a + a + b = 2a + b,

where a is the lateral side of an isosceles triangle, b is the base.

In the problem statement, we are given the values ​​of the side of the triangle and the perimeter, but it is not indicated which side is given: side or base.

This problem has 2 solutions. Let’s consider them.

The first solution to the problem.

We know the base of the triangle, b = 4 cm, and its perimeter, P = 14 cm.

Find the side:

a = (P – b) ÷ 2.

a = (14 – 4) ÷ 2 = 10 ÷ 2 = 5 cm.

Answer: the other two sides of the triangle are equal: 5 cm, 5 cm.

The second option for solving the problem.

We know the side of the triangle, a = 4 cm, and its perimeter, P = 14 cm.

This means that the second lateral side of an isosceles triangle is also 4 cm.

Find the base of the triangle:

b = P – 2a.

b = 14 – (2 × 4) = 14 – 8 = 6 cm.

Answer: the other two sides of the triangle are equal: 4 cm, 6 cm.



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