Question

The perimeter of a triangular field is 540 m, and its sides are in the ratio 25:17:12. Find the area of the field and the cost of ploughing the field at Rs. 40 per 100 m${}^2$.

• A. Area = 9000 m${}^2$ and cost = ₹3600
• B. Area = 8000 m${}^2$ and cost = ₹5000
• C. Area = 9000 m${}^2$ and cost = ₹1200
• D. Area = 6000 m${}^2$ and cost = ₹3600

Answer 1

The correct option is A Area = 9000 m${}^2$ and cost = ₹3600

Given: The perimeter of a triangular field = 540 m

Let the sides are 25x, 17x, 12 x

$\because$ The perimeter of a triangle is sum of all its sides

$\therefore$ 25x + 17x + 12x = 540

$\Rightarrow$ 54x = 540

$\Rightarrow$ x = 10

$\therefore$ Sides of the triangle are:

25x = 25$\times$10 = 250 m

17x = 17$\times$10 = 170 m and

12x = 12 $\times$ 10 = 120 m

$\text{Semi - perimeter (S)}=\frac{a+b+c}{2}=\frac{(250+170+120)}{2}=\frac{540}{2}=270m$

$\because \text{Area of a triangle}=\sqrt{s(s-a)(s-b)(s-c)}$

$\Rightarrow \text{Area}=\sqrt{270(270-250)(270-170)(270-120)}=\sqrt{270\times 20\times 100\times 150}=\sqrt{81000000}=9000{\text{m}}^2$

Given, Cost of ploughing the field at ₹40 per 100 m${}^2$
$\therefore$ cost of ploughing 1 m${}^2$ = $\frac{40}{100}$
So, cost of ploughing 9000 m${}^2$ is:
$=\frac{9000\times 40}{100}=₹3600$