Question

Mr. Dinesh owns an agricultural farm at village Talvel. The length of the farm is 10 meter more than twice the breadth. In order to harvest rain water, he dug a square shaped pond inside the farm. The side of pond is $\frac{1}{3}$ of the breadth of the farm. The area of the farm is 20 times the area of the pond. Find the length and breadth of the farm and of the pond.

Answer 1

Breadth of farm = x
Length of farm = $2x+10$
Area of farm = $lb=x\left(2x+10\right)=2x^2+10x$
Side of pond = $\frac{x}{3}$
Area of pond = $s^2={\left(\frac{x}{3}\right)}^2$
Area of farm = 2(Area of pond)
$$\begin{gathered} \Rightarrow 2x^2+10x=20\times \frac{x^2}{9} \\ \Rightarrow 18x^2+90x=20x^2 \\ \Rightarrow 9x^2+45x=10x^2 \\ \Rightarrow x^2-45x=0 \\ \Rightarrow x\left(x-45\right)=0 \\ \Rightarrow x=0,45 \end{gathered}$$
Length of farm = $2\times 45+10=100\mathrm{units}$
Breadth of farm = 45 units
Side of pond = $\frac{45}{3}=15$ units