Answer:
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.