The perimeter of the right triangle is 30 units.
The shorter leg of a right triangle is 8 less than the hypotenuse.
The longer leg is one less than the hypotenuse.
The hypotenuse is the longest side of a right triangle.
Therefore,
let
the hypotenuse = x
short leg = x - 8
long leg = x - 1
Applying Pythagorean theorem in the given right triangle.
(x - 1)² + (x - 8)² = x²
(x - 1)(x - 1) + (x - 8)(x - 8) = x²
x² - x - x + 1 + x² - 8x - 8x + 64 = x²
2x² - 18x + 65 = x²
x² - 18x + 65 = 0
(x - 13)(x - 5) = 0
Therefore,
x = 5 and x = 13
So, the hypotenuse is 13, the shorter leg is 5 and the longer leg is 12.
perimeter of the right triangle = 13 + 5 + 12 = 30
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