The shorter leg of the right triangle is 8 less than the hypotenuse. the longer leg is 1 less than the hypotenuse. find the perimeter of the triangle.

The perimeter of the triangle is 30 and this can be determined by using the Pythagorean theorem and also by using the formula of the perimeter.

Given :

Let the hypotenuse be 'H' then the shorter leg of the right triangle is (H - 8) and the longer leg is (H - 1).

Applying Pythagorean theorem in the given right triangle.

Simplify the above equation in order to determine the value of 'H'.

Factorize the above equation.

H(H - 13) - 5(H - 13) = 0

(H - 13)(H - 5) = 0

So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.

The perimeter of the triangle is given by:

P = 13 + 12 + 5

P = 30

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