#### Question

The hypotenuse of a right-angled triangle is 26 cm and the sum of other two sides is 34 cm. Find the lengths of its sides.

#### Solution

Hypotenuse = 26 cm

The sum of other two sides is 34 cm.

So, let the other two sides be x cm and (34 – x) cm.

Using Pythagoras theorem,

(26)^{2} = x^{2} + (34 – x)^{2}

676 = x^{2} + x^{2} + 1156 – 68x

2x^{2} – 68x + 480 = 0

x^{2} – 34x + 240 = 0

x^{2} – 10x – 24x + 240 = 0

x(x – 10) – 24(x – 10) = 0

(x – 10) (x – 24) = 0

x = 10, 24

When x = 10, (34 – x) = 24

When x = 24, (34 – x) = 10

Thus, the lengths the three sides of the right-angled triangle are 10 cm, 24 cm and 26 cm.

Is there an error in this question or solution?

Solution The Hypotenuse of a Right-angled Triangle is 26 Cm and the Sum of Other Two Sides is 34 Cm. Find the Lengths of Its Sides. Concept: Quadratic Equations.