Question

mr. dinesh owns an agricultural farm at village talvel. the length of the farm 10 meter more than twice the breadth. in order to harvest rain water t harvest rain water he dug square shapes pond in side the the farm. the side of pond is 1/3 of the breadth farm the area of the farm is 20 time the area of pond. find the length and breadth of the farm and of the pond

Answer 1

Check attachment......

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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