Question

The sides of a right-angled triangle are (x – 1) cm, 3x cm and (3x + 1) cm. Find:

1. the value of x,
2. the lengths of its sides,
3. its area.

Answer 1

Longer side = Hypotenuse = (3x + 1) cm

Lengths of other two sides are (x – 1) cm and 3x cm.

Using Pythagoras theorem,

(3x + 1)² = (x – 1)² + (3x)²

9x² + 1 + 6x = x² + 1 – 2x + 9x²

x² – 8x = 0

x(x – 8) = 0

x = 0, 8

But, if x = 0, then one side = 3x = 0, which is not possible.

So, x = 8

Thus, the lengths of the sides of the triangle are (x – 1) cm = 7 cm, 3x cm = 24 cm and (3x + 1) cm = 25 cm.

Area of the triangle = `1/2` × 7 cm × 24 cm = 84 cm²