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

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Question

(A) Let the sides of the triangle be $4x, 7x,$ and $9x$ meters.The perimeter of the triangle is given as $500 \, m$.Therefore,$4x + 7x + 9x = 500$.$20

Vedclass · Accepted Answer

$3750 \sqrt{5} \, m^2$

Vedclass · Answer

(A) Let the sides of the triangle be $4x, 7x,$ and $9x$ meters.The perimeter of the triangle is given as $500 \, m$.Therefore,$4x + 7x + 9x = 500$.$20x = 500 \implies x = 25$.The sides are $a = 4 	imes 25 = 100 \, m$,$b = 7 	imes 25 = 175 \, m$,and $c = 9 	imes 25 = 225 \, m$.The semi-perimeter $s = \frac{a+b+c}{2} = \frac{500}{2} = 250 \, m$.Using Heron's formula,Area $= \sqrt{s(s-a)(s-b)(s-c)}$.$s-a = 250 - 100 = 150 \, m$.$s-b = 250 - 175 = 75 \, m$.$s-c = 250 - 225 = 25 \, m$.Area $= \sqrt{250 	imes 150 	imes 75 	imes 25} = \sqrt{(25 	imes 10) 	imes (15 	imes 10) 	imes (25 	imes 3) 	imes 25}$.Area $= \sqrt{25^2 	imes 10^2 	imes 3 	imes 5 	imes 3 	imes 5} = \sqrt{25^2 	imes 10^2 	imes 3^2 	imes 5^2} = 25 	imes 10 	imes 3 	imes 5 \sqrt{5} = 3750 \sqrt{5} \, m^2$.

The sides of a triangular plot are in the ratio of $4: 7: 9$ and its perimeter is $500 \, m$. Find its area.

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