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 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 length and breadth of farm be L and B resp.

According to ques, we are given

L = 2B + 10

Area of farm = L * B

or (2B + 10) * B

Area of farm = B * (2B + 10)

Side of square pond is given to be 1/3 of breadth of farm

which is, Side = 1/3 B

Area of square pond will be = Side²

i.e. (1/3 B)²

Area of pond = 1/9 B²

Now it is given, area of farm = 20 x area of pond

So,

B * (2B + 10) = 20 x 1/9 B²

2B + 10 = 20/9 B

20/9 B - 2B = 10

20/9 B - 18/9 B = 10

2/9 B = 10

B = 45

So, L = 2(45) + 10

L = 100

and Side = 1/3 (45)

Side = 15

Therefore, L and B are 45 and 100 of farm, and Side of pond is 15

Answer 2

$<b>Answer:</b>$

100 m, 45 m, 15 m.

$<b>Step-by-step explanation:</b>$

(i)

Let the breadth of the farm be 'x' metres.

Then the length of the farm = 2x + 10.

∴ Area of the farm = x(2x + 10)

                              = $<b>2x² + 10x.</b>$

(ii)

Given that he dug a square of inside the farm, side of pond is (1/3) of breadth = (1/3) * x = (x/3).

∴ Area of pond = (x/3)²

                         = $<b>x²/9.</b>$

(iii)

Given that Area of farm is 20 times the area of pond.

⇒ 2x² + 10x = 20(x²/9)

⇒ 2x² + 10x = 20x²/9

⇒ 18x² + 90x = 20x²

⇒ -2x² = -90x

⇒ $\sf{\boxed{\boxed{x = 45.}}}$

When x = 45:

Length = 2x + 10 = 100 m

$<b>When x = 45</b>$:

Side of pond = x/3 = 15.

Therefore:

∴ $<b>Length of the farm = 100 m.</b>$

∴ $<b>Breadth of the farm = 45 m.</b>$

∴ $<b>Side of the farm = 15 m.</b>$

Hope it helps!

$\textbf{please mark as brainliest}$