Question

mr dinesh owns 1an agricultural farm at village gavel the length of the farm is 10 meter more than twice the breadth in order to harvest rain water he dug a squared shaped pond inside the farm the side of pond is1/3 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

not know what is an answer

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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