Question

The hypotenuse of a right triangle is 25 cm. The difference between the lengths of the other two sides of the triangle is 5 cm. Find the lengths of these sides.

Answer 1

Let the length of the shorter side b x cm. Then, the length of the longer side = (x + 5) cm.

Since the triangle is right-angled, the sum of the squares of the sides must be equal to the square of the hypotenuse (Pythagoras Theorem).

x² + (x + 5)² = 235²

or x² + x² + 10x + 25 = 625 

or 2x² + 10x - 600 = 0

or x² + 5x - 300 = 0 

or (x + 20) (x - 15) = 0

This gives x = 15 or x = - 20 

We reject x = - 20 and take x = 15.

Thus, length of shorter side = 15 cm. 

Length of longer side = (15 + 5) cm, i.e., 20 cm.