Find the side of an isosceles triangle if the base is 18 cm and the area is 108 cm2.

1. Vertices of the triangle – A, B, C. BE – height. S – area. AC = 18 cm.

2. We calculate the length of the height BE, using the formula for calculating the area of a triangle:

S = AC x BE / 2.

BE = 2 x 108/18 = 12 cm.

3. According to the properties of an isosceles triangle, the height BE is also the median and

divides the base into two equal segments:

AE = CE = 18: 2 = 9 cm.

4. AB = √AE² + BE² (by the Pythagorean theorem).

AB = √9² + 12² = √81 + 144 = √225 = 15 cm.

Answer: the length of the side of the triangle is 15 cm.