Find the side of an isosceles triangle if its base is 18 cm and its area is 108 cm.

An isosceles triangle is a triangle in which the sides are equal.

Knowing the length of the base and the area of this triangle, we find its height:

S = 1/2 * a * h;

h = 2S / a, where:

S is the area of the triangle;

a – the base of the speaker;

h – HV height.

h = 108 * 2/18 = 216/18 = 12 cm.

Consider the triangle ΔАВН. To calculate the lateral side AB, we apply the Pythagorean theorem:

AB ^ 2 = BH ^ 2 + AH ^ 2;

AH = AC / 2;

AH = 18/2 = 9 cm;

AB2 = 122 + 92 = 144 + 81 = 225;

AB = √225 = 15 cm.

Answer: the length of the lateral side AB is 15 cm.