Question

The hypotenuse of a right-angled triangle exceeds one side by 1 cm and the other side by 18 cm; find the lengths of the sides of the triangle.

Answer 1

Let one hypotenuse of the triangle be x cm.

From the given information,

Length of one side = (x – 1) cm

Length of other side = (x – 18) cm

Using Pythagoras theorem,

x² = (x – 1)² + (x – 18)²

x² = x² + 1 – 2x + x² + 324 – 36x

x² – 38x + 325 = 0

x² – 13x – 25x + 325 = 0

x(x – 13) – 25(x – 13) = 0

(x – 13)(x – 25) = 0

x = 13, 25

When x = 13, x – 18 = 13 – 18 = –5, which being negative, is not possible.

So, x = 25

Thus, the lengths of the sides of the triangle are x = 25 cm, (x – 1) = 24 cm and (x – 18) = 7 cm.