Find the sides of an isosceles triangle if its perimeter = 54 cm and the height to the base is 9 cm

Let the lateral side of a given isosceles triangle be expressed through the variable a.

Consequently, the length of its base can be represented using the expression 54 – 2a.

And its half is like 27 – a.

But after all, from the conditions of this task, we know for sure that the height that is drawn to the base is 9 cm, so we can write down the equation and find the lengths of the sides:

a ^ 2 – 9 ^ 2 = (27 – a) ^ 2;

a ^ 2 – 81 = 729 – 54a + a ^ 2;

54a = 810;

a = 15;

54 – 2 * 15 = 24.

Answer: Lateral 15 cm, base – 24 cm.