Question

square and rectangle have same perimeter if the side of squareis 60 cm and length of rectangle is 80 m which has more area​

Answer 1

☯︎ Given that,

• $\sf \: Square \: and \: rectangle \: have \: same \: perimeter.$
• $\sf \: Side \: of \: square \: is \: \bold{60cm}$
• $\sf \: Length \: of \: the \: rectangle \: is \: \bold{80cm}$

☯︎ We have to find,

• $\sf \: Which \: has \: more \: area \: ?$

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★ Firstly, we'll find the perimeter of the square.

$\boxed{\boxed{\bold\purple{perimeter \: of \: a \: square = 4 \times side}}}$

$\sf\implies \: perimeter \: of \: the \: square \: = 4 \times side \\ \\ \sf\implies \: perimeter \: of \: the \: square \: = 4 \times 60 \\ \\ \sf\implies \: perimeter \: of \: the \: square \: = \boxed{\boxed{\sf\purple{240cm}}}\bigstar$

★ Now, we'll find the perimeter of the rectangle.

$\boxed{\boxed{\bold\purple{perimeter \: of \: a \: rectangle \: = \: 2(length \: + \: breadth)}}}$

Put the value of perimeter of the square in the formula.

$\sf\implies \: perimeter \: of \: the \: rectangle \: = 2(l + b) \\ \\ \sf\implies \: 240 = 2(80 + b) \\ \\ \sf\implies \: \: \frac{240}{2} = 80 + b \\ \\ \sf\implies \: 120 = 80 + b \\ \\ \sf\implies \: 120 - 80 = b \\ \\ \sf\implies \: b = \boxed{\boxed{\sf\purple{40cm}}}\bigstar$

★ Now, we'll find the area of the rectangle.

$\boxed{\boxed{\bold\purple{area \: of \: a \: rectangle \: = length \: \times breadth}}}$

$\sf\implies \: area \: of \: the \: rectangle \: = l \times b \\ \\ \sf\implies \: area \: of \: the \: rectangle \: = 40 \times 80 \\ \\ \sf\implies \: area \: of \: the \: rectangle \: \: = \boxed{\boxed{\sf\purple{3200 {cm}^{2} }}}\bigstar$

★ Now, find the area of the square.

$\boxed{\boxed{\bold\purple{area \: of \: a \: square \: = {side}^{2} }}}$

$\sf\implies \: area \: of \: the \: square \: = {side}^{2} \\ \\ \sf\implies \: area \: of \: the \: square \: = {60}^{2} \\ \\ \sf\implies \: area \: of \: the \: square \: = \boxed{\boxed{\sf\purple{3600 {cm}^{2} }}}\bigstar$

$\sf \: 3600 > 3200$

$\sf\therefore\underline{Hence, \: the \: area \: of \: the \: square \: is \: more \: than \: the \: area \: of \: the \: rectangle.}$

Answer 2

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

➟ Square and rectangle have same perimeter

➟ Side of square is 60 cm

➟ Length of rectangle is 80 cm

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

➟ Which has more area

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

$\:\:\:\: \bigstar \: \large{\boxed{\boxed{\sf{\pink{Formula\:used\:here\::}}}}}$

1. Perimeter of square = 4 × side
2. Perimeter of rectangle = 2(l + b)
3. Area of square = side × side
4. Area of rectangle = length × breadth

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$\:\:\:\: \large \underline {\sf{Perimeter\:of\:square\::}}$

➟ 4 × side

➟ 4 × 60

➟ 240 cm

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• It is mentioned both have same perimeter , so perimeter of rectangle is also equal to 240 cm

$\:\:\:\: \large \underline {\sf{Breadth\:of\:Rectangle\::}}$

➟ Perimeter = 2(l + b)

➟ 240 = 2 ( 80 + b )

➟ 240/2 = 80 + b

➟ 120 = 80 + b

➟ b = 120 - 80

➟ Breadth = 40 cm

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$\:\:\:\: \large \underline {\sf{Area\:of\:square\::}}$

➟ side × side

➟ 60 × 60

➟ 3600 cm²

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$\:\:\:\: \large \underline {\sf{Area\:of\: rectangle\::}}$

➟ length × breadth

➟ 80 × 40

➟ 3200 cm²

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$\:\:\:\: \bigstar \: \underline {\sf{\pink{Square\:has\:larger\:area\:by\:400\:{cm}^{2}}}}$

• And we are done !

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