Question

the area of a square and rectangle are equal if the side of the square is 30 centimetre and the breadth of the rectangle is 20 cm find the length of the rectangle also find the perimeter of the rectangle​

Answer 1

Working out:

In the question, we are provided that the area of a square and the area of a rectangle is equal. Side of the square is also given and breadth of the rectangle is also given.

• Area of square = Area of rectangle
• Side of the square = 30 cm
• Breadth of the square = 20 cm

To find the length and the perimeter of the rectangle.

For finding the above answers, first we need to know how to find the area of square and rectangle, Perimeter of Square and rectangle.

• Area of square = side²
• Area of rectangle = length × breadth
• Perimeter of square = 4 × side
• Perimeter of rectangle = 2(Length + breadth)

So, let's solve by using formula,

⇛ Area of the square = Area of the rectangle

⇛ side² = length × breadth

Plug in the given values,

⇛ 30² cm² = length × 20 cm

⇛ length = 900 cm² / 20 cm

⇛ length = 45 cm

Now finding the perimeter,

⇛ Perimeter of rectangle = 2(l + b)

⇛ Perimeter = 2(45 + 20) cm

⇛ Perimeter = 2(65) cm

⇛ Perimeter = 130 cm

So, our length and perimeter of the rectangle respectively are:

$\large{ \boxed{ \sf{ \red{45 \: cm \: and \: 130 \: cm}}}}$

And we are done !!

Answer 2

Given:

• Area of square= Area of rectangle
• Side of square= 30cm
• Breadth of rectangle= 20cm

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Need to Find:

• Length of rectangle =?
• Perimeter of rectangle =?

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Solution:

Area of square= ${side}^{2}$

⟹ Area of square= 30cm ×30cm

⟹ Area of square= 900${cm}^{2}$

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Area of square= Area of Rectangle

⟹ 900${cm}^{2}$ = length× breadth

⟹length× 20cm = 900 ${cm}^{2}$

⟹length= 900÷ 20cm

⟹$\red{\bold{Length= 45cm}}$

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Perimeter of rectangle

= 2×(length+breadth)

=2× (45+20) cm

= 2× 65cm

=130cm

$\red{\bold{\therefore Perimeter=130cm}}$