Question

A square has the same area as that of a rectangle of length and breadth equal to 244cm and 61 cm respectively . Find the perimeter of the square.​

Answer 1

Answer:

Perimeter of square = 488 $cm^{2}$

Step-by-step explanation:

According to the information provided in the question it is given as

A square has the same area as that of a rectangle of length and breadth equal to 244 cm and 61 cm respectively .

We need to find find the perimeter of the square.​

Area of square = l  x b (rectangle )  (Given in question)

                         = 244 x 61

                         = 14884$cm^{2}$

Area of rectangle = Area of square

14884 = $a^{2}$ (where a is side of square)

$\sqrt{14884} = a\\122 cm =a$

Hence side of square  = 122 cm

Now we find perimeter of square

Perimeter of square = 4 a

Substituting the value we get the answer

$P = 4 \times 122\\P = 488cm^{2}$

Hence perimeter of square is 488 $cm^{2}$

Answer 2

Answer :-

$\\\;\large{\underbrace{\underline{\textsf{Question's Analysis\;:-}}}}$

The Area of a Rectangle, Area of a Square and the Perimeter of a Square have been used in this question. The area of a square is equal to the perimeter of a rectangle, according to the question. A rectangle's length and breadth are specified. We are meant to work out the square's perimeter. We will start by calculating the area of the rectangle, then use the given condition to calculate the square's perimeter.

Let's do it !!

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Formulas used :-

$\\\;\boxed{\sf{\:Area_{(Rectangle)}=\bf{length \times breadth\;}}}$

$\\\;\boxed{\sf{\:Area_{(Square)}=\bf{(side)^2\;}}}$

$\\\;\boxed{\sf{\:Perimeter_{(Square)}=\bf{4(side)\;}}}$

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Solution :-

Given that,

» Length of a rectangle = l = 244cm

» Breadth of a rectangle = b = 61cm

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~ Finding the area of a rectangle ::

• Length = 244cm

• Breadth = 61cm

$\;\implies\sf{\;Area_{(Rectangle)} = 244 \times 61}$

$\\\;\implies\sf{\;Area_{(Rectangle)} = \bf{14884}}$

Thus, the area of a rectangle is 14884cm².

~ Using the given condition ::

As it is given that, the area of a rectangle is equal to the area of a square. Therefore,

$\;\implies\sf{\;Area_{(Rectangle)}=Area_{(Square)}}$

$\\\;\implies\sf{\;14884=(side)^2}$

$\\\;\implies\sf{\;side=\sqrt{14884}}$

$\\\;\implies\sf{\;side=\bf{112}}$

Thus, the side of a square is 112cm.

~ Finding the perimeter of square ::

• Side = 112cm

By using the perimeter of square formula, and substituting the side value in it, we get:

$\;\implies\sf{\;Perimeter_{(Square)}=4(side)}$

$\\\;\implies\sf{\;Perimeter_{(Square)}=4(112)}$

$\\\;\implies\bf{\;Perimeter_{(Square)}=488}$

Hence, the perimeter of the square is 488cm.

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More formulas to know :-

• Diagonal of square = side√2

• Diagonal of rectangle = √[(length)² + (breadth)²]

• Length of rectangle = Area/Breadth

• Breadth of rectangle = Area/Length