The perimeter of an isosceles triangle is 16cm, and its base is 6cm. Find the height drawn to the base of the triangle.

An isosceles triangle is a triangle in which the sides are equal: AB = BC.

The length of a triangle is the sum of all its sides:

P = AB + BC + AC.

AB = BC = (P – AC) / 2;

AB = BC = (16 – 6) / 2 = 10/2 = 5 cm.

The height of an isosceles triangle, lowered to the base, divides it in half:

AH = HC = AC / 2;

AH = HC = 6/2 = 3 cm.

In order to calculate the length of the BH height, consider the triangle ΔAVH. This triangle is right-angled, so we apply the Pythagorean theorem:

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

BH ^ 2 = AB ^ 2 – AH ^ 2;

BH ^ 2 = 5 ^ 2 – 3 ^ 2 = 25 – 9 = 16;

BH = √16 = 4 cm.

Answer: The length of the HV height is 4 cm.