Question

The perimeter of a right-triangular field is 540 m and its sides are in the ratio 25 : 17 : 12. Find the area of the field. Also, find the cost of ploughing the field at Rs 18.80 per 100 m².

Answer 1

Let the sides of the triangular field be 25x m , 17x m and 12x m.
Perimeter is the sum of all the sides. Therefore,

$$\begin{gathered} 25x+17x+12x=540 \\ \Rightarrow 54x=540 \\ \Rightarrow x=\frac{540}{54}=10 \end{gathered}$$

The lengths of the sides are:

$$\begin{gathered} a=25x=25\times 10=250\mathrm{m} \\ b=17x=17\times 10=170\mathrm{m} \\ c=12x=12\times 10=120\mathrm{m} \\ \mathrm{Semi}\mathrm{perimeter}\left(\mathrm{s}\right)\mathrm{of}\mathrm{the}\mathrm{triangle}=\frac{540}{2}=270\mathrm{m} \\ \mathrm{Area}\mathrm{of}\mathrm{the}\mathrm{triangle}=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)} \\ =\sqrt{270\left(270-250\right)\left(270-170\right)\left(270-120\right)} \\ =\sqrt{270\times 20\times 100\times 150} \\ =\sqrt{81000000} \\ =9000{\mathrm{m}}^2 \end{gathered}$$

The cost of ploughing is Rs. 18.80 per 100 m².

The cost of ploughing 9000 m²

$=\frac{9000\times 18.80}{100}=\mathrm{Rs}.1692$


Thus, it costs Rs. 1692 to plough a field of area 9000 m².