An isosceles triangle has sides A, B, and C, such that sides A and B have the same length. Side C has a length of #16 # and the triangle has an area of #128 #. What are the lengths of sides A and B?
The area of the triangle is
In an isosceles triangle the altitude to the base forms two congruent right triangles. In each right triangle:
1) One leg of the right triangle is the altitude, in this case
2) The other leg is half the base of the isosceles triangle, in this case
3) The hypoteneuse of the right triangle is one leg of the isosceles triangle. Thus using the Pythagorean theorem: