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(A) Let the sides of the triangle be $a = 85 \, m$,$b = 154 \, m$,and $c$ be the third side.Given perimeter $P = 324 \, m$.So,$c = P - (a + b) = 324 -

Vedclass · Accepted Answer

$27720$

Vedclass · Answer

(A) Let the sides of the triangle be $a = 85 \, m$,$b = 154 \, m$,and $c$ be the third side.Given perimeter $P = 324 \, m$.So,$c = P - (a + b) = 324 - (85 + 154) = 324 - 239 = 85 \, m$.The semi-perimeter $s = \frac{P}{2} = \frac{324}{2} = 162 \, m$.Using Heron's formula,the area of the triangle is $\sqrt{s(s-a)(s-b)(s-c)}$.Area $= \sqrt{162(162-85)(162-154)(162-85)} = \sqrt{162 	imes 77 	imes 8 	imes 77}$.Area $= \sqrt{162 	imes 8 	imes 77^2} = \sqrt{1296 	imes 5929} = 36 	imes 77 = 2772 \, m^2$.The cost of ploughing at the rate of ₹ $10$ per $m^2$ is $2772 	imes 10 = ₹ 27720$.

Two sides of a triangular field are $85 \, m$ and $154 \, m$,respectively,and its perimeter is $324 \, m$. The cost of ploughing the field at the rate of ₹ $10$ per $m^2$ is (in ₹):

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