The area of a triangle is 216 , cm^{2} and it | vedclass

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(D) Let the sides of the triangle be $3x$,$4x$,and $5x$.The semi-perimeter $s$ is given by $s = \frac{3x + 4x + 5x}{2} = \frac{12x}{2} = 6x$.Using Her

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$72$

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(D) Let the sides of the triangle be $3x$,$4x$,and $5x$.The semi-perimeter $s$ is given by $s = \frac{3x + 4x + 5x}{2} = \frac{12x}{2} = 6x$.Using Heron's formula,the area $\Delta$ is $\sqrt{s(s-a)(s-b)(s-c)}$.$\Delta = \sqrt{6x(6x-3x)(6x-4x)(6x-5x)} = \sqrt{6x \cdot 3x \cdot 2x \cdot x} = \sqrt{36x^{4}} = 6x^{2}$.Given that the area is $216 \, cm^{2}$,we have $6x^{2} = 216$.$x^{2} = 36$,which implies $x = 6 \, cm$.The perimeter of the triangle is $3x + 4x + 5x = 12x$.Perimeter $= 12 	imes 6 = 72 \, cm$.

The area of a triangle is $216 \, cm^{2}$ and its sides are in the ratio $3:4:5$. The perimeter of the triangle is ....... $cm$.

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