SOLUTION: In a 45°-45°-90° triangle where the hypotenuse measures m, find the area of the triangle

Algebra ->  Triangles -> SOLUTION: In a 45°-45°-90° triangle where the hypotenuse measures m, find the area of the triangle       Log On


   

Question 593943: In a 45°-45°-90° triangle where the hypotenuse measures m, find the
area of the triangle
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If the legs are x, then x%5E2%2Bx%5E2=2x%5E2=m%5E2


So in short, 2x%5E2=m%5E2. Now solve for x to get x+=+sqrt%28m%5E2%2F2%29+=+%28m%2Asqrt%282%29%29%2F2

This means that the leg 'x' is x+=+%28m%2Asqrt%282%29%29%2F2

Now use this to find the area:

A+=%28bh%29%2F2

A+=%28%28%28m%2Asqrt%282%29%29%2F2%29%2A%28%28m%2Asqrt%282%29%29%2F2%29%29%2F2

A+=%28m%5E2%2Asqrt%282%2A2%29%29%2F%282%2A2%2A2%29

A+=%28m%5E2%2Asqrt%284%29%29%2F%288%29

A+=%28m%5E2%2A2%29%2F%288%29

A+=%28m%5E2%29%2F%284%29


Therefore, if the hypotenuse is 'm' units long, then the area of the 45-45-90 degree triangle is