Question

An isosceles triangle has side lengths of 16, an altitude of x, and a base of 2x. Find the length of the base.

Answer 1

Explanation:

Since the altitude of an isosceles triangle drawn from its vertex angle bisects the base, we can use the pythagorean theorem to say that:

16^2 = x^2 + x^2

256 = 2x^2

128=x^2

x = 8sqrt2.

so the base has a length of 16sqrt2.