The sides of a triangular plot are in the rat | vedclass

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(C) Let the sides of the triangle be $3x, 5x$ and $7x$ meters.The perimeter of the triangle is given as $300\, m$.Therefore,$3x + 5x + 7x = 300$.$15x

Vedclass · Accepted Answer

$1500\sqrt{3}\, m^2$

Vedclass · Answer

(C) Let the sides of the triangle be $3x, 5x$ and $7x$ meters.The perimeter of the triangle is given as $300\, m$.Therefore,$3x + 5x + 7x = 300$.$15x = 300$,which gives $x = 20$.Thus,the sides of the triangle are $3 	imes 20 = 60\, m$,$5 	imes 20 = 100\, m$,and $7 	imes 20 = 140\, m$.Using Heron's formula,the semi-perimeter $s$ is:$s = \frac{60 + 100 + 140}{2} = \frac{300}{2} = 150\, m$.The area of the triangle is $\sqrt{s(s-a)(s-b)(s-c)}$.Area $= \sqrt{150(150 - 60)(150 - 100)(150 - 140)}\, m^2$.Area $= \sqrt{150 	imes 90 	imes 50 	imes 10}\, m^2$.Area $= \sqrt{6750000}\, m^2$.Area $= 1500\sqrt{3}\, m^2$.

The sides of a triangular plot are in the ratio of $3 : 5 : 7$ and its perimeter is $300\, m$. Find its area.

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