#### 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.

#### Solution

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}

9x^{2} + 1 + 6x = x^{2} + 1 – 2x + 9x^{2}

x^{2} – 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 = ½ × 7 cm × 24 cm = 84 cm²

Is there an error in this question or solution?

Solution 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. Concept: Quadratic Equations.