Question

The area of square and rectangle are equal . If the side of the square is 30 cm and length of rectangle is 50 cm , then find perimeter of rectangle ?
plz anss​

Answer 1

$\large\sf\underline{Given\::}$

• Area of a square and rectangle is equal.

• Length of square = 30 cm.

• Length of Rectangle = 50 cm.

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$\large\sf\underline{To\:find\::}$

• Perimeter of the rectangle.

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$\large\sf\underline{Creating\:the\:road\:map\:for\:Solution\::}$

In this question we are told that the area of square = area of rectangle. The length of side of square is 30 cm and the length of rectangle is 50 cm. We are asked to find the perimeter of rectangle. So we do know that Perimeter of rectangle = 2 ( l + b ) . But wait , we do know the length of the rectangle but we don't have the value of its breadth.

So what can be done ? And yeah it's simple we will use the relation that area of square = area of rectangle. From this we will get the breadth of rectangle and we can easily substitute it's value in the formula and end up getting our final result that is the Perimeter of the rectangle. Let's proceed !

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$\large\sf\underline{Formula\:to\:be\:used\::}$

• $\small{\mathfrak\red{Area\:of\:square\:=\:(side)^{2}}}$

• $\small{\mathfrak\red{Area\:of\:rectangle\:=\:length \times breadth}}$

• $\small{\mathfrak\red{Perimeter\:of\:rectangle\:=\:2(length + breadth)}}$

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$\large\sf\underline{Solution\::}$

According to the question :

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Area of square = Area of rectangle

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

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• Substituting the given values

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$\sf\implies\:(30) ^{2} = 50 \times breadth$

$\sf\implies\:900 = 50 \times breadth$

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• Transposing 50 to the other side

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$\sf\implies\:\cancel{\frac{900}{50}}= breadth$

$\small{\underline{\boxed{\mathrm\pink{\implies\:Breadth\:=\:18\:cm}}}}$

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So now let's find the perimeter of rectangle :

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$\sf\implies\:Perimeter\:of\:rectangle\:=\:2(l+b)$

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• Let's substitute the values

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$\sf\implies\:Perimeter\:of\:rectangle\:=\:2(50+18)$

$\sf\implies\:Perimeter\:of\:rectangle\:=\:2(68)$

$\small{\underline{\boxed{\mathrm\pink{\implies\:Perimeter\:of\:rectangle\:=\:136\:cm}}}}$ ★

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$\dag\:\underline{\sf So\:the\:required\:perimeter\:of\:rectangle\:is\:136\:cm}$

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_____________________________

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$\large\sf\underline{Some\:formula\:regarding\:Perimeter:}$

• Perimeter of square = $\sf\:4 × length$

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• Perimeter of rectangle = $\sf\:2 (length+breadth)$

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• Perimeter of right angled triangle = $\sf\:a+b+c$

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• Perimeter of equilateral triangle = $\sf\:3 × side$

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• Perimeter of circle = $\sf\:2πr$

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!! Hope it helps !!

Answer 2

Square:

Side of Square = a= 30cm

Then area of the Square= side × side =a²

Area of the Square = 30cm × 30cm

Area of Square = 900cm²

━━━━━━━━━━━━━━━━

Rectangle

Given, length = 50cm

Let, the breadth of the rectangle be = b cm

Area of a rectangle = length × breadth

→ Area of the rectangle = 50 cm × b

━━━━━━━━━━━━━━━━

Now given,

Now given,Area of Square = Area of rectangle

Thus,

Thus,→ 900cm² = 50cm × b

Thus,→ b= 900 ÷ 50 cm

Thus,→ b= 900 ÷ 50 cm→ b = 18cm

Perimeter of a rectangle = 2 × (length + breadth)

→ Perimeter= 2×(50 + 18) cm

→ Perimeter = 2× 68cm

→ Perimeter of the rectangle=136cm.

hope it's helpful,,,,,

@—

OP Boy