Question

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Mr. Dinesh owns an agricultural farm. The length of the farm is 10 metres more than twice the breadth. In order to harvest rainwater, he dug a square shaped pond inside the farm. The side of the pond is 1/3 of the breadth of the farm. The area of the farm is 20 times the area of pond. Find the length and breadth of the farm and of the pond. ​

Answer 1

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for farm,

length = 100 m

breadth = 45 m

for pond,

side = 15 m

step-by-step explanation:

Let,

the length of the farm be ' l '

the breadth of the farm be ' b '

and

the side length of the pond be 'a '

Now,

A.T.Q,

length of the farm is 10 metres more than twice the breadth

=> l = 2b + 10 ................(i)

also,

side of the pond is 1/3 of the breadth of the farm

=> a = b/3 ...............(ii)

again,

area of the farm is 20 times the area of pond

=> l × b = 20(${a}^{2}$)

putting the values of 'l' and 'a' from eqn (i) and (ii),

we get,

=> b × (2b + 10) = 20 ${(b/3)}^{2}$

=> 2${b}^{2}$ + 10b = 20${b}^{2}$/9

doing cross- multiplication,

we get,

=>18 ${b}^{2}$ + 90b= 20${b}^{2}$

=> 2${b}^{2}$ - 90b = 0

=> 2b(b - 45) = 0

=> b = 0 or b = 45

°.° b is length , it can't be 0

.°. b = 45 m

Now,

putting the value of b in eqn (i),

we get,

l = 2×45 + 10 = 90+10 = 100 m

again,

putting the value of b in eqn (ii),

we get,

a = 45/3 = 15 m

Answer 2

Answer:

100 m, 45 m, 15 m.

Step-by-step explanation:


(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)

                              = 2x² + 10x.



(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

                         = x²/9.



(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

⇒ x = 45.

When x = 45:

Length = 2x + 10 = 100 m

When x = 45:

Side of pond = x/3 = 15.



Therefore:

∴ Length of the farm = 100 m.

∴ Breadth of the farm = 45 m.

∴ Side of the farm = 15 m.



Hope it helps!