In an isosceles triangle, the base is half the side and the perimeter is 50 cm. Find the sides of the triangle.

| September 18, 2021 | education

We denote by x the length of the base of this isosceles triangle, and by y – the length of the lateral side of this triangle.

According to the condition of the problem, the length of the base in this triangle is two times less than the lateral side, therefore, we can write the following relation:

x = 2 * y.

It is also known that the perimeter of this triangle is 50 cm, therefore, we can write the following ratio:

x + y + y = 50.

We solve the resulting system of equations.

Substituting into the second equation the value x = 2 * y from the first equation, we get:

2 * y + y + y = 50.

We solve the resulting equation:

4 * y = 50;

y = 50/4;

y = 12.5 cm.

Knowing the length of the side, we find the length of the base x:

x = 2 * y = 12.5 * 2 = 25 cm.

Answer: the base length is 12.5 cm, the side length is 25 cm.



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