Question

wire is in shape of rectangle. its length is 32 CM and breadth is 18 CM. if same wire is rebent in shape of square, what will be measure of each side? also, find which shape encloses more area​

Answer 1

$\star \; {\underline{\boxed{\pmb{\gray{\sf{ \; Given \; :- }}}}}}$

• Length of Rectangle = 32 cm
• Breadth of Rectangle = 18 cm

$\star \; {\underline{\boxed{\pmb{\orange{\sf{ \; To \; Find \; :- }}}}}}$

• Side of Square = ?

$\star \; {\underline{\boxed{\pmb{\color{cyan}{\sf{ \; SolutioN \; :- }}}}}}$

${\pmb{\color{maroon}{\frak{ Note \; :- }}}}$

$\longrightarrow$ In this question we must remember that if the Shape of something is changed their is no change in its Perimeter .

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$\dag$ Formula Used :

• ${\underline{\boxed{\sf{ Perimeter{\small_{(Rectangle)}} = 2 \bigg( Length + Breadth \bigg) }}}}$

• ${\underline{\boxed{\sf{ Perimeter{\small_{(Square)}} = 4 \times Side }}}}$

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$\dag$ Calculating the Perimeter of Rectangle :

${\longmapsto{\qquad{\sf{ Perimeter = 2 \bigg( Length + Breadth \bigg) }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Perimeter = 2 \bigg( 32 + 18 \bigg) }}}} \\ \\ \\ \ {\longmapsto{\qquad{\sf{ Perimeter = 2 \times 50 }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\pink{\frak{ Perimeter = 100 \; cm }}}}}}}}$

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$\dag$ Calculating the Side of Square :

${\dashrightarrow{\qquad{\sf{ Perimeter = 4 \times Side }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 100 = 4 \times Side }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{100}{4} = Side }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{100}{4} = Side }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\pmb{\purple{\frak{ Side = 25 \; cm }}}}}}}}$

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$\dag$ Therefore :

❛❛ Side of the Square will be 25 cm . ❜❜

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Answer 2

$\purple{According \: to \: the \: question,} \\ \purple{Perimeter \: of \: square=Perimeter \: of \:rectangle }\\ \purple{⇒4× side=2(length+breadth)}\\ \purple{⇒4 \times side = 2(32 + 18)}\\\purple{⇒4 \times side = 2 \times 50}\\ </p><p>\purple{⇒Side = \frac{2 \times 50}{4}= 25cm} \\ \purple{ Thus, the \: side \: of \: the \: square \: is \: 25cm. }\\\red{Now,} \\ \purple{Area \: of\:rectangle=length×breadth=32×18=576cm²} \\ \purple{ And \: Area \: of \: square=side×side=25×25=625cm²} \\ \purple{Therefore, on \: comparing, the \: area \: of \: square \: is \: greater \: than \: that \: of \: rectangle.}$