The hypotenuse of a right triangle is 6 m more than twice the shortest side. If the third side is 2m less than the hypotenuse, find the sides of the triangle.

Let the shortest side be x meters.

Hypotenuse = 2x + 6 meters

Third side = 2x + 6 - 2 = 2x + 4 meters.

Since, the sides are of a right triangle.

By pythagoras theorem,

⇒ (Hypotenuse)² = (First Side)² + (Second side)²

⇒ (2x + 6)² = (x)² + (2x + 4)²

⇒ 4x² + 36 + 24x = x² + 4x² + 16 + 16x

⇒ 4x² + 36 + 24x = 5x² + 16 + 16x

⇒ 5x² - 4x² + 16x - 24x + 16 - 36 = 0

⇒ x² - 8x - 20 = 0

⇒ x² - 10x + 2x - 20 = 0

⇒ x(x - 10) + 2(x - 10) = 0

⇒ (x + 2)(x - 10) = 0

⇒ x = -2 or x = 10.

Since, side cannot be negative,

x ≠ -2.

Shortest side = 10 m

Hypotenuse = 2x + 6 = 2(10) + 6 = 26 m

Third side = 2x + 4 = 2(10) + 6 = 24 m.

Hence, sides of triangle = 10 m, 24 m and 26 m.