SOLUTION: Please help me solve this: Find the formula for the area of an isosceles right triangle in terms of the hypotenuse? all i know is that A=1/2bh... but i do not know what to do wi

Algebra ->  Triangles -> SOLUTION: Please help me solve this: Find the formula for the area of an isosceles right triangle in terms of the hypotenuse? all i know is that A=1/2bh... but i do not know what to do wi      Log On


   

Question 168206This question is from textbook
: Please help me solve this: Find the formula for the area of an isosceles right triangle in terms of the hypotenuse?
all i know is that A=1/2bh... but i do not know what to do with it. Thank you in advance! This question is from textbook

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
First, to draw an isosceles right triangle, draw a square, then draw one of its diagonals. You now have two congruent isosceles right triangles.
Now draw the other diagonal and you will see that the diagonals of a square bisect each other.
Next, erase one of the triangles (that's half the square) and you are left with one isosceles right triangle whose height (h) is exactly half the length of its base (b). But the base is really the hypotenuse of this right triangle. So, for the area of this triangle, you can write:
A+=+%281%2F2%29bh But h+=+%281%2F2%29b, so substitute this to get:
A+=+%281%2F2%29b%2A%281%2F2%29b Simplify.
A+=+%281%2F4%29b%5E2 where b is the length of the hypotenuse.