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

Solution:

The problem is summarized in the figure below:

Using the Pythagorean theorem:

c² = a² + b² (where c = hypotenuse and a, b the other two sides of the right angled triangle)

L² = (L - 8)² + (L - 1)²

L² = L² + 64 - 16L + L² + 1 - 2L

L² - 18L + 65 = 0

L = [18 ± √18² - 4(1)(65)]/(2)(1)

L = 9 ± √324 - 260]/(2)(1)

L = 9 ± √64/2 = 9 ± 8/2 = 9 ± 4 = 13 or 5

L = 5 cannot be possible because shorter side is 8 less than the hypotenuse. 5 - 8 will be negative.

Therefore L = hypotenuse = 13

The shorter side is 13 - 8 = 5

The longer side is 13 - 1 = 12

Hence the perimeter is 5 + 12 + 13 = 30

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

Summary:

The short leg of a right triangle is 8 less than the hypotenuse. The longer leg is 1 less than the hypotenuse. The perimeter of the triangle is 30