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?

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Answer 1 · 2016-04-15T23:54:19

#8\sqrt{5}# units.

The area of the triangle is #128#. The base is #16#. So the altitude to the base is

#h=2((128)/16)=16#.

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 #16#.

2) The other leg is half the base of the isosceles triangle, in this case #8#.

3) The hypoteneuse of the right triangle is one leg of the isosceles triangle. Thus using the Pythagorean theorem:

#\sqrt{16^2+8^2}=\sqrt{320}=8\sqrt{5}#