SOLUTION: A right triangle has a perimeter of 32 and an area of 20. what is the length of the hypotenuse?

Question 242783: A right triangle has a perimeter of 32 and an area of 20. what is the length of the hypotenuse?
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
1) a+b+c=32
.
2)
(a*b)/2=20
a*b=40
a=40/b
.
1)
c=32-b- 40/b substitute 40/b for a.
c=(32b-b^2-40)/b
.
3)
a^2+b^2=c^2
(40/b)^2+b^2
=1600/b^2+b^2
.
1600/b^2 + b^2 = ((32b-b^2-40)/b)^2
1600/b^2 + b^2 = b^2-64b- 2560/b + 1600/b^2+1104
1600+b^4=b^4-64b^3-2560b+1600+1104b^2
-64b^3+1104b^2-2560b=0
-16b(4b^2-69b+160)=0
4b^2-69b+160=0
b=2.76..., b=14.49 (both legs, actually)
2.76^2+14.49^2=217.56
sqrt(217.5625)=14.75 Hypotenuse
That was a tough one!
.
Ed
.
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