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.

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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)   (Show Source): You can put this solution on YOUR website!

let the hypotenuse be
if the shorter leg of a right triangle is less than the hypotenuse, we have
if the longer leg is less than the hypotenuse, we have


the perimeter is:




Answer by ikleyn(52803)   (Show Source): You can put this solution on YOUR website!
.

Let H be the hypotenuse length.


Then your equation is


     +  = .


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.


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