(Q8) The hypotenuse of a right triangle is 6m more than twice of the shortest side. If the third side is 2 m., less than the hypotenuse, find the sides of the triangle.

Solution :

Let the shortest side be x m.

Then hypotenuse = (2x + 6)m and third side = (2x + 4)m

By Pythagores theorem, we have

(2x + )² = x² + (2x + )²

x² + x + = x² + 4x² + x +

x² - x - = 0

x = or x =

But x can't be negative as it is a side of a triangle.

∴ x =

Hence, the sides of the triangle are m, m and m.