Find the height of an isosceles triangle if its sides are 68 and the base is 64.

1. Vertices of the triangle – A, B, C. AB = BC = 68 units. AC = 64 units. BК – height.

2. The height of BK in an isosceles triangle also serves as a median, that is, it divides the AC side into two identical segments:

AK = CK = 64: 2 = 32 units.

3. We calculate the length of the height BK using the formula of the Pythagorean theorem:

BK = √AB² -AK² = √68² -32² = √4624 – 1024 = √3600 = 60 units.

Answer: the length of the height BK is 60 units of measurement.