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 Rs 10 per $m^{2}$ is ____.

Rs. 27720

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Rs. 37620

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Rs. 26750

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Rs. 26954

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None of these

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Solution

The correct option is A Rs. 27720
The third side of the triangle $= 324 - (85 + 154) = 85 m .$
Also, $s = \frac{a + b + c}{2} = \frac{324}{2} = 162.$
$∴$ Area of the triangle
$= \sqrt{s (s - a) (s - b) (s - c)} = \sqrt{162 (162 - 85) (162 - 85) (162 - 154)} = \sqrt{162 \times 77 \times 77 \times 8} = 2772 m^{2} .$
$∴$ The cost of ploughing the field
$= 2772 \times 10$ =Rs. 27720

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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 Rs 10 per m2 is ____.

The correct option is A Rs. 27720The third side of the triangle =324−(85+154)=85m. Also, s=a+b+c2=3242=162. ∴ Area of the triangle =√s(s−a)(s−b)(s−c)=√162(162−85)(162−85)(162−154)=√162×77×77×8=2772m2. ∴ The cost of ploughing the field =2772×10 =Rs. 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 Rs 10 per $m^{2}$ is ____.