In a certain isosceles right triangle, the altitude to the hypotenuse has length . what is the area of the triangle?

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

i can't see the picture : /

i believe the correct answer is option 4.principalities were small territories that were run by russian rulers.

which statement correctly defines principalities in northern asia in the 1200s? principalities were small territories that were run by russian rulers.

hope i could ! : )