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 one side of the right triangle be x cm

So, the other side will be = (x + 5) cm [as they differ by 5cm]

And given that hypotenuse = 25 cm

On applying Pythagoras Theorem, we have

x² + (x + 5)² = 25²

x² + x² + 10x + 25 = 625

2x² + 10x + 25 – 625 = 0

2x² + 10x – 600 = 0

x² + 5x – 300 = 0

x² – 15x + 20x – 300 = 0 [By factorisation method]

x(x – 15) + 20(x -15) = 0

(x – 15)(x + 20) = 0

x = 15 or x = – 20 (neglected) As the side of triangle can never be negative.

Thus, when x = 15 ⇒ x + 5 = 15 + 5 = 20

Hence, the length of side of right triangle is 15 cm and other side is 20 cm