SOLUTION: The hypotenuse of an isosceles right triangle measures 15 feet. Find the area.

Algebra ->  Customizable Word Problem Solvers  -> Geometry -> SOLUTION: The hypotenuse of an isosceles right triangle measures 15 feet. Find the area.       Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 259881: The hypotenuse of an isosceles right triangle measures 15 feet. Find the area.
Found 2 solutions by Earlsdon, Alan3354:
Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
The area of the triangle is given by:
A+=+%281%2F2%29%28b%2Ah%29 but in an isosceles right triangle, b = h, so we'll just say that b = x and h = x, so the area is:
A+=+%281%2F2%29x%5E2
Now to find x, we'll use the Pythagorean theorem where c (the hypotenuse) = 15 ft.
15%5E2+=+x%5E2%2Bx%5E2
225+=+2x%5E2
x%5E2+=+112.5 Substitute into the equation for the area:
A+=+%281%2F2%29x%5E2
A+=+%281%2F2%29%28112.5%29
highlight%28A+=+56.25%29sq.ft.

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
15^2 = 2s^2
Area = s^2/2 = 225/4
Area = 56.25 sq feet