SOLUTION: a right triangle has an area of 60 m^2 and the hypotenuse is 2 m longer than the longer side of 2 remaining legs. Can you please find the dimensions of the triangle?

Algebra ->  Triangles -> SOLUTION: a right triangle has an area of 60 m^2 and the hypotenuse is 2 m longer than the longer side of 2 remaining legs. Can you please find the dimensions of the triangle?      Log On


   

Question 318709: a right triangle has an area of 60 m^2 and the hypotenuse is 2 m longer than the longer side of 2 remaining legs. Can you please find the dimensions of the triangle?
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1.A=%281%2F2%29L1%2AL2=60
2.H=L2%2B2
From the Pythagorean theorem,
3.L1%5E2%2BL2%5E2=H%5E2
From eq. 1,
L1%2AL2=120
L1=120%2FL2
Substitute into eq. 3,
%28120%2FL2%29%5E2%2BL2%5E2=%28L2%2B2%29%5E2
%28120%2FL2%29%5E2%2BL2%5E2=L2%5E2%2B4L2%2B4
%2814400%2FL2%5E2%29=4L2%2B4
14400=4L2%5E3%2B4L%5E2
L2%5E3%2BL2%5E2-3600=0
You can factor this equation,
%28L2-15%29%28L2%5E2%2B16L2%2B240%29=0
One real solution:
L2-15=0
highlight%28+L2=15%29
.
.
L1=120%2F15
highlight%28+L1=8%29
.
.
H=L2%2B2
highlight%28+H=17+%29