SOLUTION: One leg of a right triangle is 2 m longer than the other leg. The length of the hypotenuse is 10 m.Find the lenght of each side.

Algebra ->  Pythagorean-theorem -> SOLUTION: One leg of a right triangle is 2 m longer than the other leg. The length of the hypotenuse is 10 m.Find the lenght of each side.      Log On


   

Question 231199: One leg of a right triangle is 2 m longer than the other leg. The length of the hypotenuse is 10 m.Find the lenght of each side.
Found 2 solutions by checkley77, jsmallt9:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
x^2+(x+2)^2=10^2
x^2+x^2+4x+4=100
2x^2+4x+4-100=0
2x^2+4x-96=0
2(x^2+2x+48)=0
2(x+8)(x-6)=0
x-6=0
x=6 m. for the shorter side.
6+2=8 m. for the longer side.
Proof:
6^2+8^2=10^2
36+64=100
100=100

Answer by jsmallt9(3758) About Me  (Show Source):
You can put this solution on YOUR website!
Let x = the shorter leg.
Then x+2 = the longer leg.
Therefore, by the Pythagorean Theorem:
%28x%29%5E2+%2B+%28x%2B2%29%5E2+=+%2810%29%5E2
Now we just solve this. This is a quadratic equation (because of the x%5E2 terms so we will simplify:
x%5E2+%2B+x%5E2+%2B+4x+%2B+4+=+100
2x%5E2+%2B+4x+%2B+4+=+100
... get one side equal to zero ...
2x%5E2+%2B+4x+-+96+=+0
... factor ...
2%28x%5E2+%2B+2x+-+48%29+=+0
2%28x+%2B+8%29%28x-6%29+=+0
... use the Zero Product Property to find what values make the product zero ...
x%2B8+=+0 or x-6+=+0
Solving these is simple:
x+=+-8 or x+=+6
Since x represents the shorter leg we must reject x = -8 because we don't have negative lengths for legs. So the only acceptable length for the shorter leg is 6. And this makes the longer leg 8 (because it is 2 meters longer).

In summary, the sides of the triangle are 6, 8 and 10 meters long.