Question

The area of a rectangle and square are equal. If the side of square is 60cm and length of

rectangle is 45cm.Find breadth of rectangle.​

Answer 1

Solution

Given:-

• Area of rectangle = Area of Square
• Side of square = 60 cm
• Length of rectangle = 45 cm

Find :-

• Breadth of rectangle

Explanation

Using Formula

$\dag\boxed{\underline{\tt{\red{\:Area_{rectangle}\:=\:(Length\times Breadth)}}}}$

$\dag\boxed{\underline{\tt{\green{\:Area_{Square}\:=\:(Side)^2}}}}$

First Calculate Area of Square,

==> Area of square = (Side)²

==> Area of square = 60²

==> Area of square = 3600

According to question,

==> Area of rectangle = Area of Square

==> (45 × Breadth) = 3600

==> Breadth = 3600/45

==> Breadth = 80

Hence

• Area of rectangle will be = 80 cm

___________________

Answer 2

Given : The area of the rectangle and square are equal and the side of square is 60cm and length of the rectangle is 45cm.

To Find : Breadth of the rectangle.

⠀⠀⠀⠀⠀⠀⠀⠀ ⠀⠀____________________

Here, side of the square is given as 60cm and length of the rectangle is given as 45cm. It is also given that area of the rectangle is equal to the area of the square. So, firstly we'll find the area of the square and then we'll put the value of area in the area of the rectangle formula.

$\:$

As we know that :

$\: \:$

$\star \: \underline{\boxed{\sf\pink{Area_{(square)} = {side}^{2} }}}$

$\: \:$

Now, we'll put the value of side of square in the formula.

$\:$

$\sf:\implies \: Area_{(square)} = {side}^{2} \\ \\ \\ \sf:\implies \: Area_{(square)} = {(60)}^{2} \\ \\ \\ \sf:\implies \: Area_{(square)} = 60 \times 60 \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{Area_{(square)} = 3600 \: {cm}^{2}}}} \: \bigstar$

$\: \:$

As we've got the area, So we'll apply area of the rectangle formula.

$\: \:$

Area of the rectangle :

$\: \:$

$\star \: \underline{\boxed{\sf\pink{Area_{rectangle} = l \times b}}} \:$

$\: \:$

Where, l denotes length of the rectangle and b denotes breadth of the rectangle.

$\: \:$

$\sf:\implies \: Area_{(rectangle)} = l \times b \\ \\ \\ \sf:\implies \: 3600 = 45 \times b \\ \\ \\ \sf:\implies \: b = \cancel\frac{3600}{45} \\ \\ \\ \sf:\implies \: \underline{\boxed{\mathfrak\purple{b = 80cm}}} \: \bigstar \: \\ \\ \\ \\ \sf\therefore{\underline{Hence, \: the \: breadth \: of \: the \: rectangle \: is \: \bold{80cm}.}}$