Question

the perimeter of a triangular fields is 1080m and it's side are in the ratio 25:17:12.find the area of the triangle also find the cost of ploughing the field rate rs 18.80 per 20 so.metre​

Answer 1

$\sf \Large Solution!!$

Let the ratio be 25x, 17x and 12x.

Perimeter = 1080 m

So,

Perimeter = Sum of all three sides.

1080 m = 25x + 17x + 12x

1080 m = 54x

x = 1080 m ÷ 54

x = 20 m

Therefore, 25x = 25 × 20 m = 500 m

17x = 17 × 20 m = 340 m

12x = 12 × 20 m = 240 m

Verifying.

500 m + 340 m + 240 m = 1080 m

1080 m = 1080 m

Hence, verified.

Now, we know the sides of the triangle. We can easily find out the area by Heron's formula.

Semi-perimeter (s) = $\sf \dfrac{a+b+c}{2}$

$\sf s=\dfrac{500\:m+340\:m+240\:m}{2}$

$\sf s=\dfrac{1080\:m}{2}$

$\sf s=540\:m$

$\sf$

$\sf Area=\sqrt{s(s-a)(s-b)(s-c)}$

$\sf Area=\sqrt{540(540-500)(540-340)(540-240)}$

$\sf Area=\sqrt{540\times 40\times 200\times 300}$

$\sf Area=\sqrt{1296\times 10^{6}}$

$\sf Area=36,000\:m^{2}$

Cost of ploughing 20 m² = Rs 18.80

Cost of ploughing 1 m² = Rs 0.94

Cost of ploughing 36,000 m² = Rs 33,840