The longer leg of a right triangle is 3m longer than the shorter leg. The hypotenuse is 6m longer than the shorter leg. Find the side lengths of the triangl

Step-by-step explanation:

Let x represent the the length of the shorter leg of the right angle triangle.

The longer leg of a right triangle is 3m longer than the shorter leg. It means that that the length of the longer leg is (x + 3) m.

The hypotenuse is 6m longer than the shorter leg. It means that the hypotenuse of the longer leg is (x + 6) m.

We would apply Pythagoras theorem which is expressed as

(x + 6) ² = x² + (x + 3) ²

(x + 6) (x + 6) = x² + (x + 3) (x + 3)

x² + 6x + 6x + 36 = x² + x² + 3x + 3x + 9

x² + 12x + 36 = 2x² + 6x + 9

2x² - x² + 6x - 12x + 9 - 36 = 0

x² - 6x - 27 = 0

x² + 3x - 9x - 27 = 0

x (x + 3) - 9 (x + 3) = 0

x - 9 = 0 or x + 3 = 0

x = 9 or x = - 3

Since the length cannot be negative, then

Length of the shortest side is 9 m.

Length of the longer side is 9 + 3 = 12 m

Length of the hypotenuse is 9 + 6 = 15 m.