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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.
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Solution
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)
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