#### 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.

#### Solution

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,

x^{2} = (x – 1)^{2} + (x – 18)^{2}

x^{2} = x^{2} + 1 – 2x + x^{2} + 324 – 36x

x^{2} – 38x + 325 = 0

x^{2} – 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.

Is there an error in this question or solution?

Solution 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. Concept: Quadratic Equations.