Question

Mr Dinesh owns an agricultural farm at village talvel . The length of The farm is 10 meter more than twice it's breadth. In order to harvest rainwater 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 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!

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