SOLUTION: In a right triangle, one leg is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the length of the sides of the triangle.

Algebra ->  Triangles -> SOLUTION: In a right triangle, one leg is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the length of the sides of the triangle.      Log On


   

Question 1075003: In a right triangle, one leg is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the length of the sides of the triangle.
Found 3 solutions by addingup, ikleyn, MathTherapy:
Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
one leg: x
other leg: x-7
hypotenuse: x+2
x+x-7+x+2 = perimeter
3x-5 = perimeter
Substitute in these operations with the information you have NOT provided, I'm guessing it's either the length of one of the legs or the perimeter. Email me if you need more help.
:
John

Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
.
Your equation is Pythagorean

x%5E2+%2B+%28x-7%29%5E2 = %28x%2B2%29%5E2.


Simplify and solve for x:

x%5E2+%2B+x%5E2+-+14x+%2B+49 = x%5E2+%2B+4x+%2B+4,

x%5E2+-+18x+%2B+45 = 0.


Factor left side:

(x-3)*(x-15) = 0.


The root x = 15 is appropriate.
The root x = 3 is EXTRANEOUS solution, since x-7 is negative in this case.

The sides of the triangle are 15, x-7 = 8  and  x+2 = 17.


Answer. The sides are 8, 15 and 17.


Check.  8%5E2+%2B+15%5E2 = 289 = 17%5E2.  Correct !


Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!
In a right triangle, one leg is 7 feet shorter than the other leg. The hypotenuse is 2 feet longer than the longer leg. Find the length of the sides of the triangle.