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.Solve the word problem

Answer 1

Answer:

45 * 100 m

15 * 15 m

Step-by-step explanation:

Let say Breadth of Farm =  3B  m

The length of the farm is 10 meter more than twice the breadth.

The Length of Farm = 2(3B) + 10  = 6B + 10 m

Area of Farm = 3B(6B + 10) m²

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

Breadth Of Pond = (1/3)3B = B m

Pond is Square shaped so length & Breadth are equal

So Area of Pond  = B²

area of the farm is 20 times the area of the pond

=> 3B(6B + 10) = 20B²

=> 18B + 30 = 20B

=> 2B = 30

=> B = 15

Pond Length & Breadth=  15 m each

Breadth Of Farm = 3B = 3*15 =  45 m

Length of Farm = 6B + 10 = 6*15 + 10 = 100 m

Answer 2

Answer:

Breadth=45meter

length=100meter

Step-by-step explanation:

let the breadth of the farm be X

therefore Length=2X+10

Since Pond is of square shape with side $\frac{1}{3}rd$ of breadth

i.e $\frac{1}{3}X$

area of pond=$(side)^{2}$

area of pond=$(\frac{1}{3}X)^{2} = \frac{1}{9}X^{2}$

given area of farm is 20 times area of pond

therefore,area of farm=$\frac{20}{9}X^{2}$

Also area of farm=L×B

$\frac{20}{9}X^{2}$=(2X+10)X

$\frac{20}{9}X^{2}=2X^{2}+10X$

$\frac{20}{9}X^{2}-2X^{2}=-10X$

$2X^{2}=90X$

$2X^{2}-90X=0$

X(2X-90)=0

X=0(not possible)

X=45

therefore breadth=45m

length=2×45+10=100m