SOLUTION: The shorter leg of a right triangle is 7 foot shorter than the longer leg. The hypotenuse is 7 foot longer than the longer leg. Find the side lengths of the triangle.

Algebra ->  Pythagorean-theorem -> SOLUTION: The shorter leg of a right triangle is 7 foot shorter than the longer leg. The hypotenuse is 7 foot longer than the longer leg. Find the side lengths of the triangle.       Log On


   

Question 1006899: The shorter leg of a right triangle is 7 foot shorter than the longer leg. The hypotenuse is 7 foot longer than the longer leg. Find the side lengths of the triangle.
Answer by vleith(2983) About Me  (Show Source):
You can put this solution on YOUR website!
The legs are x (x+7) and (x+14)
Since it is a right triangle, you know Pythagorean applies
a%5E2+%2B+b%5E2+=+c%5E2
x%5E2+%2B+%28x%2B7%29%5E2+=+%28x%2B14%29%5E2
x%5E2+%2B+x%5E2+%2B+14x+%2B+49+=+x%5E2+%2B+28x+%2B+196
2x%5E2+%2B+14x+%2B+49+=+x%5E2+%2B+28x+%2B+196
x%5E2+-14x+-+147+=+0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-14x%2B-147+=+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=%28-14%29%5E2-4%2A1%2A-147=784.

Discriminant d=784 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--14%2B-sqrt%28+784+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-14%29%2Bsqrt%28+784+%29%29%2F2%5C1+=+21
x%5B2%5D+=+%28-%28-14%29-sqrt%28+784+%29%29%2F2%5C1+=+-7

Quadratic expression 1x%5E2%2B-14x%2B-147 can be factored:
1x%5E2%2B-14x%2B-147+=+1%28x-21%29%2A%28x--7%29
Again, the answer is: 21, -7. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-14%2Ax%2B-147+%29


Since the length cannot be negative, then x = 21.
Sides are 21, 28, and 35 feet