Question

The sides of a right-angled triangle containing the right angle are 4x cm and (2x – 1) cm. If the area of the triangle is 30 cm²; calculate the lengths of its sides.

Answer 1

Area of triangle = 30 cm²

∴ `1/2 xx (4x) xx (2x - 1) = 30`

`2x^2 - x = 15`

`2x^2 - x - 15 = 0`

`2x^2 - 6x + 5x - 15 = 0`

`2x(x - 3) + 5(x - 3) = 0`

`(x - 3)(2x + 5) = 0`

`x = 3, (-5)/2`

But, x cannot be negative, so x = 3

Thus, we have

AB = 4 × 3 cm = 12 cm

BC = (2 × 3 – 1) cm = 5 cm

CA = `sqrt(12^2 + 5^2)  cm` = 13 cm  ...(Using Pythagoras theorem)