SOLUTION: Find the lengths of the sides if a right triangle if we know that the longer leg is 2 feet longer than the shorter leg, while the hypotenuse is 5 feet longer than the shorter leg.

Question 971441: Find the lengths of the sides if a right triangle if we know that the longer leg is 2 feet longer than the shorter leg, while the hypotenuse is 5 feet longer than the shorter leg. Set up the equation that models the relationship and then solve
Answer by amarjeeth123(569) (Show Source): You can put this solution on YOUR website!
Let the shorter leg be x.
Then the longer leg is (x+2).
Then the hypotenuse is (x+5).
In a right angled triangle we have square of the hypotenuse is equal to sum of squares of the other two sides.
(x+5)^2=(x+2)^2+x^2
x^2+10x+25=x^2+4x+4+x^2
x^2+10x+25=2x^2+4x+4
x^2-6x-21=0

Solved by pluggable solver: SOLVE quadratic equation with variable

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=120 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 8.47722557505166, -2.47722557505166. Here's your graph:

We have x=8.477
The shorter leg is 8.477 feet.
The longer leg is 10.477 feet.
The hypotenuse is 13.477 feet.
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