SOLUTION: The shorter leg of a right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. Find the perimeter.

Algebra ->  Triangles -> SOLUTION: The shorter leg of a right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. Find the perimeter.       Log On


   

Question 1153739: The shorter leg of a right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. Find the perimeter.
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

let the hypotenuse be x
if the shorter leg of a right triangle is 8 less than the hypotenuse, we have x-8
if the longer leg is 1+less than the hypotenuse, we have
x-1

the perimeter is:
P=x%2B%28x-8%29%2B%28x-1%29
P=x%2Bx-8%2Bx-1
P=3x-9

Answer by ikleyn(52800) About Me  (Show Source):
You can put this solution on YOUR website!
.

Let H be the hypotenuse length.


Then your equation is


    %28H-8%29%5E2 + %28H-1%29%5E2 = H%5E2.


Solve this quadratic equation and find H.


Then evaluate the lengths of the legs (H-8) and (H-1).


By knowing the sides of the triangle, you will find its perimeter.


ANSWER.  It is the Pythagorean triangle (5, 12, 13) with the perimeter of 30 units.