In a certain iscoceles right triangle, the altitude to the hypotenuse has length 4. What is the area of the triangle?

The altitude to the hypotenuse will divide the original triangle into two isosceles right triangles.

Since the altitude is 4, the base of each of these two new triangles will also be 4, making the base of

the original triangle 8.

Area = 1/2 x 8 x 4 = 16