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(C) The area of a right-angled triangle is given by the formula: $	ext{Area} = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Given,$	ext{base

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$12 \, m, 14 \, m$

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(C) The area of a right-angled triangle is given by the formula: $	ext{Area} = \frac{1}{2} 	imes 	ext{base} 	imes 	ext{height}$.Given,$	ext{base} = x \, m$ and $	ext{height} = (x+2) \, m$.$	ext{Area} = 84 \, m^2$.So,$84 = \frac{1}{2} 	imes x 	imes (x+2)$.$168 = x^2 + 2x$.$x^2 + 2x - 168 = 0$.Factoring the quadratic equation: $x^2 + 14x - 12x - 168 = 0$.$x(x+14) - 12(x+14) = 0$.$(x-12)(x+14) = 0$.Since the length cannot be negative,$x = 12$.The sides are $x = 12 \, m$ and $x+2 = 14 \, m$.

The lengths of the sides forming the right angle of a right-angled triangle are $x \, m$ and $(x+2) \, m$. If the area of the triangle is $84 \, m^2$,find the lengths of the sides which form the right angle.

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