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

Let $l$ be the length of the farm and $b$ be the breadth.

Then, according to the question,

$l=10+2b$

Let $x$ be the side of the pond, then,

$x=\frac{1}{3}b$

The area of the square pond is,

$A={\left(\frac{1}{3}b\right)}^2$

$A=\frac{1}{9}{b}^2$

The area of the farm is,

$A=l\times b$

$A=\left(10+2b\right)\left(b\right)$

$A=10b+2b^2$

According to the question,

$Areaofthefarm=20\left(areaofthepond\right)$

$10b+2b^2=20\left(\frac{1}{9}{b}^2\right)$

$90b+18b^2=20b^2$

$2b^2-90b=0$

$2b\left(b-45\right)=0$

$2b=0$

$b=0$

Or,

$b=45$

Since the breadth cannot be 0, so the breadth of the farm is $45m$. Then, the length is,

$l=10+2\left(45\right)$

$l=100m$

Therefore, the length of the farm is $100m$ and the breadth of the farm is $45m$.