One leg of a right triangle is 6 millimeters longer than the shorter leg and the hypotenuse is 12 millimeters longer than the shorter leg. Find the lengths of the sides of the triangle.

Question

plz oh plz help

Answer 1

Let x: length of the shorter leg

(x + 6): length of the longer leg

(x + 12): length of hypotenuse

By Pythag Thm:

x² + (x + 6)² = (x + 12)²

x² + x² + 12x + 36 = x² + 24x + 144

x² - 12x - 108 = 0

(x - 18)(x + 6) = 0

x = 18 or -6 but -6 is not a valid solution

Side lengths are 18, 24, and 30. (A 3-4-5 right triangle (Egyptian triangle) scaled up by a factor of 6.)