In a certain isosceles right triangle, the altitude to the hypotenuse has length 4 √(2) . what is the area of the triangle?

Question

In a certain isosceles right triangle, the altitude to the hypotenuse has length


`4 √(2)`
. what is the area of the triangle?

Answer 1

32

The step by step things are on the picture.

It doesn't look very clear so click on the pic.

Answer 2

The angle bisector, median, and altitude are all the same things in an isosceles triangle.

That means that the legs of the smaller triangles created by the altitude are 4 root 2.

By special properties of an right triangle, the hypotenuse is 8.

Since the legs of the original right triangle are congruent, the area of the original triangle is 8*8/2.

Now we just simplify:

8*8/2=64/2=32