SOLUTION: This is another word problem question. One leg of a right triangle is 96 inches. Find the hypothesis and the other leg if the length of the hypotenuse exceeds 2 1/2 times the other

Question 139101: This is another word problem question. One leg of a right triangle is 96 inches. Find the hypothesis and the other leg if the length of the hypotenuse exceeds 2 1/2 times the other leg by 4 inches.
>>>i tried working it out and got 2 1/2 times leg + 4 eguals hypotenuse
and 2 1/2 divided leg - 4 eguals leg.
Answer by edjones(8007) (Show Source): You can put this solution on YOUR website!
Let a=96, c=2.5b+4
a^2+b^2=c^2
96^2+b^2=(2.5b+4)^2
9216+b^2=6.25b^2+20b+16
5.25b^2+20b-9200=0
b=40" (see below)
c=2.5*40+4=104"
.
Check:
9216+1600=10816
104^2=10816
.
Ed
.

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=193600 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 40, -43.8095238095238. Here's your graph:

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