#### 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.

#### Solution

Area of triangle = 30 cm^{2}

`∴ 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 x 3 cm = 12 cm

BC = (2 x 3 - 1) cm = 5 cm

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

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Solution 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. Concept: Quadratic Equations.