I was doing a problem in which I was told the lengths of all sides of an isosceles triangle and asked to find the area.
I solved the problem by dividing the isosceles triangle into two equal triangles to find the height which I used in the area formula for the original triangle.
Looking at the answer, my method resulted in the correct value but, it seems I could have used the legs of the isosceles triangle (both 8) as the base and height and skipped finding the height. Why does that shortcut work? The question is below:
If the hypotenuse of an isosceles right triangle is $8 \sqrt 2$, what is the area of the triangle?
- (A) 18
- (B) 24
- (C) 32
- (D) 48
- (E) 64