SOLUTION: The hypotenuse of a right triangle is 11 miles long. One leg of the triangle is 3 miles longer than the other leg. Find the sum ofo the lengths of the two legs of the right trian

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Question 112968: The hypotenuse of a right triangle is 11 miles long. One leg of the triangle is 3 miles longer than the other leg. Find the sum ofo the lengths of the two legs of the right triangle.
Answer by edjones(8007)   (Show Source): You can put this solution on YOUR website!
Let a be b+3
a^2+b^2=c^2
(b+3)^2+b^2=11^2
b^2+6b+9+b^2=121
2b^2+6b-112=0
2(b^2+3b-56)=0
b=6.13217... mi (see below)
a=9.13217... mi
Check:
9.13217^2+6.13217^2=121
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=233 is greater than zero. That means that there are two solutions: .




Quadratic expression can be factored:

Again, the answer is: 6.13216876123687, -9.13216876123687. Here's your graph:
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