Question

2. The area of a square is 225 sq. cm. Find its perimeter.

3. The cost of fencing a square garden at the rate of 75 per metre is 2,000. Find the area of the garden.


4. The cost of ploughing a square farm is the same as ploughing another farm that is rectangular in shape. The rate of ploughing is the
same in both the cases. The side of the square farm is 20 m and the length of the rectangular farm is 40 m. Find the breadth of the farm.​

Answer 1

Answer:

perimeter of square =4xsquare

4x 225=1020

Answer 2

2. Given:-

• Area of square = 225 sq.cm

To find:-

• Its perimeter.

Solution:-

We know,

$\sf{Area \:of\:a\:square = (side)^2}$

=> $\sf{225 = (side)^2}$

=> $\sf{Side = \sqrt{225}}$

=> $\sf{Side = 15\:cm}$

Now,

$\sf{Perimeter\:of\:a\:square = (4\times Side) \: units}$

=> $\sf{Perimeter = (4 \times 15)\:cm = 60\:cm}$

=> $\sf{Perimeter = 60\:cm\: [Answer]}$

$\sf{\therefore The\:perimeter\:of\:the\:square\:is\:60\:cm}$

_____________________________________________

3. Given:-

• Cost of fencing a square garden at the rate of Rs.75 per metre is Rs.2000.

To find:-

• Area of the square.

Solution:-

$\sf{Cost\: of \:fencing\: a\: square\: garden\: at\: Rs.75\: per\: metre\: is\: Rs.2000}$

$\sf{Perimeter \:of \:the \:garden = \dfrac{Cost\:of\:fencing\:the\:garden}{Cost\:per\:metre}}$

$\sf{Perimeter = \dfrac{2000}{75}}$

$\sf{Perimeter = 26.67 m}$

We know,

$\sf{Perimeter\:of\:a\:Square = (4\times Side)\:units}$

=$\sf{26.67 = 4\times Side}$

=>$\sf{Side = \dfrac{26.67}{4}}$

=> $\sf{Side = 6.67\:m}$

Now,

$\sf{Area = (side)^2\:sq.units}$

= $\sf{Area = (6.67)^2\: m^2}$

=> $\sf{Area = 4.49\: m^2\:\:[Approx]}$

$\sf{\therefore The\:Area\:of\:the\:garden\:is\:4.49\:m^2\:[Approximately]}$

_____________________________________________

4. Given:-

• Cost of ploughing the square field is equal to the cost of ploughing a rectangular field.
• Side of a square field = 20m
• Length of rectangular field = 40m

To find:-

• Breadth of the rectangular field.

Solution:-

$\sf{Side\: of \:square \:field = 20\:m}$

We know,

$\sf{Area\:of\:a\:square = (side)^2 \:sq.units}$

Therefore,

$\sf{Area\:of\:the\:square\:field = (20)^2\:m^2}$

$\sf{Area = 400 m^2}$

Now,

ATQ

$\sf{Cost\:of\:ploughing\:rectangular\:field = Cost\:of\:ploughing\:square\:field}$

$\sf{It\:means\:Area\:of\:both\:the\:fields\:is\:same}$

Therefore,

$\sf{(side)^2 = length\times breadth}$

=> $\sf{400 = 40 \times breadth}$

=> $\sf{Breadth = \dfrac{400}{40}\:m}$

=> $\sf{Breadth = 10\:m \:(Answer)}$

$\sf{\therefore The\: breadth \:of\: the\: rectangular\: field\: is\: 10\: m}$

_____________________________________________