In an isosceles triangle, the side is 10cm, and its base is 16cm, then the height lowered to the base is?

1. Vertices of the triangle – A, B, C. AB = BC = 10 centimeters. BH is the height drawn to the base.

2. According to the properties of an isosceles triangle, the BH height is also the median and divides the base of the AC into two equal segments.

AH = CH = AC: 2 = 16: 2 = 8 centimeters.

3. In a right-angled triangle ABH, the height BH is a leg. Its length is calculated using the Pythagorean theorem:

BH = √AB² – AH² = √10² – 8² = √100 – 64 = √36 = 6 centimeters.

Answer: The length of the height BH is 6 centimeters.