Question

The perimeter of a triangular field is $540m$ and its sides are in the ratio $25:17:12$ Find the area of the triangle. Also find the cost of ploughing the field at $Rs20$ per $10m^2$

Answer 1

Step 1: Finding the sides of the triangle

Perimeter of triangle $=540cm$
Let the sides of the triangle be, $25x,17xand12x.$

$\begin{array}{l}25x+17x+12x=540\\ 54x=540\\ x=\frac{540}{54}\\ x=10\\ 25x=25\times 10=250cm\\ 17x=17\times 10=170cm\\ 12x=12\times 10=120cm\end{array}$

Step 2: Finding the area of the triangle, using the Heron's formula

$\begin{array}{l}A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ a=250cm,b=170cm,c=120cm\\ \therefore s=\frac{a+b+c}{2}\\ s=\frac{250+170+120}{2}\\ s=\frac{540}{2}\\ s=270\\ A=\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}\\ A=\sqrt{270\left(270-250\right)\left(270-170\right)\left(270-120\right)}\\ A=\sqrt{270\left(20\right)\left(100\right)\left(150\right)}\\ A=9000c{m}^2\end{array}$

Step 3: Finding the cost of ploughing the field

The cost of ploughing $10m^2=Rs20$
The cost of ploughing $1m^2=\frac{20}{10}$

Therefore, the cost of ploughing $9000m^2=9000\times \left(\frac{20}{10}\right)$

$\begin{array}{l}\Rightarrow 9000\times 2\\ \Rightarrow 18000cm\end{array}$

Hencce, the area of the triangle is $9000c{m}^2$ and the cost of ploughing the the field at $Rs20$ per $10m^2$ is $Rs18000$.