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.

Question

Mathematics

Evony

28 August, 07:11

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.

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Phoebe Castillo · Answer 1

Hypotenuse = h

leg1 = h-8

leg2 = h-1

h² - (h-8) ² = (h-1) ²

h² - [h² - 16h + 64] = h² - 2h + 1

16h - 64 = h² - 2h + 1

h² - 18h + 65 = 0

hypotenuse = 13

leg1 = 13-8 = 5

leg2 = 13-1 = 12

Perimeter = 13 + 5 + 12 = 30