Question

1) Find the length of the side of the following squares, given the area.
a) Area = 225 sq. m
b Area = 81 sq.mm

2) Find the length of the other side of the rectangle, given the area and one of its sides.
a) area = 6750 sq.m;
side=75 m
b) area = 1575 sq. cm;
side=45 cm​

Answer 1

1st Answer :

To Solve this question we need to know about the formula required to find the area of the square.

That is,

Area of the square = side x side

= side^2

So,

Now using this formula we are going to find the measurement of the side.

Coming back to the question

From the above we came to know that,

Side^2 = Area of the square

a) Area of the square = 225 m^2

Side of the square = ?

Then , Let the side be " x " meters

$x \times x = 225 \\ {x}^{2} = 225 \\ x = \sqrt{225} \\ x = 15 \: meters$

Therefore,

side of the square = x = 15 meters.

b) Area of the square = 81 m^2

Side of the square = ?

Then, Let the side be " x " meters

$x \times x = 81 \\ {x}^{2} = 81 \\ x = \sqrt{81} \\ x = 9 \: meters$

Therefore,

side of the square = x = 9 meters.

2nd Answer :

To Solve this question we need to know about the formula required to find the area of the rectangle

That is,

Area of the rectangle = Length x breadth

So,

Now using this formula we are going to find the measurement of the side.

Coming back to the question

From the above we came to know that,

Length x breadth = Area of the rectangle

a) Area of the rectangle = 6750 m^2

side = 75 m ( let this as the length)

Hence,

Let the breadth be " x " meters.

$75 \times x = 6750 \\ x = \frac{6750}{75} \\ x = 90 \: meters$

Therefore,

The breadth = 90 meters.

b) Area of the rectangle = 1575 m^2

side = 45 m ( let this as the length)

Hence,

Let the breadth be " x " meters.

$45 \times x = 1575 \\ x = \frac{1575}{45} \\ x = 35 \: meters$

Therefore,

The breadth = 35 meters

Answer 2

We know that ,

The area of square is given by

$\large \mathbb{ \fbox{AREA = {(SIDE)}^{2} </p><p>}}$

The area of rectangle is given by

$\large \mathbb{\fbox{AREA = LENGTH \times BREADTH}}$

First Question

(A) Given ,

Area of the square = 225 m²

Thus ,

225 = (side)²

side = √225

side = 15 m

(B) Given ,

Side of square = 81 m²

Thus ,

81 = (side)²

side = √81

side = 9 m

Second Question

(A) Given ,

The area of rectangle and one of its side are 6750 m² and 75 m

Thus ,

6750 = length × 75

length = 6750/75

length = 90 m

(B) Given ,

The area of rectangle and one of its side are 1575 m² and 45 m

Thus ,

1575 = length × 45

length = 1575/45

length = 35 m