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.

Algebra ->  Graphs -> 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.       Log On


   

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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-6x%2B-21+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%28-6%29%5E2-4%2A1%2A-21=120.

Discriminant d=120 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--6%2B-sqrt%28+120+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-6%29%2Bsqrt%28+120+%29%29%2F2%5C1+=+8.47722557505166
x%5B2%5D+=+%28-%28-6%29-sqrt%28+120+%29%29%2F2%5C1+=+-2.47722557505166

Quadratic expression 1x%5E2%2B-6x%2B-21 can be factored:
1x%5E2%2B-6x%2B-21+=+1%28x-8.47722557505166%29%2A%28x--2.47722557505166%29
Again, the answer is: 8.47722557505166, -2.47722557505166. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-6%2Ax%2B-21+%29

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.