Question

Find the side of a square whose perimeter is equal to the perimeter of a regular pentagon of side 5.6cm ?

Answer 1

Given:- The perimeter of a regulat Pentagon is equivalent to that of the perimeter of a square. The side of Pentagon is 5.6 cm and we are asked to find the side of square.

Concept:- First we'll find the perimeter of Pentagon. Then we'll equate it to the perimeter of square and will find the required value.

Formula:-

• Perimeter of Pentagon = 5 × sides

• Perimeter of Square = 4 × sides

Solution :-

➜ perimeter of Pentagon = 5 × sides

➜ perimeter of Pentagon = 5 × 5.6 cm

➜ perimeter of Pentagon = 28 cm

Now, equate this value of perimeter of Pentagon to that of square and find the answer.

➜ perimeter of square = 4 × side

➜ 28 = 4 × side

➜ side = 28 ÷ 4

➜ side = 7 cm

hence, the required side of the square is 7 cm.

_______________________

Answer 2

Given : The Perimeter of Regular Pentagon whose sides are 5.6 cm long is equal to Perimeter of Square.

Need To Find : The Length of Side of Square ?

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❍ Let's say , that the Length of Side of Square be a cm.

$\\\\ \:\:\bigstar \:\:\underline {\pmb{\boldsymbol { \: According \:To\:The \:Question \:\::\:}}}\:$

⠀⠀⠀▪︎ The Perimeter of Regular Pentagon whose sides are 5.6 cm long is equal to Perimeter of Square .

$\\ \dashrightarrow \sf \:\Big\{\:Perimeter_{\:( Regular \: Pentagon \:)}\:\Big\}\:\:=\:\Big\{ \:Perimeter _{\:( Square)}\:\Big\}$

• Perimeter of Pentagon : 5 × Side

$\dashrightarrow \sf \:\Big\{\:5\:\times \:Side\:\Big\}\:\:=\:\Big\{ \:Perimeter _{\:( Square)}\:\Big\}$

$\dashrightarrow \sf \:\Big\{\:5\:\times \:Side\:\Big\}\:\:=\:\Big\{ \:Perimeter _{\:( Square)}\:\Big\}$

• Perimeter of Square : 4 × Side

$\dashrightarrow \sf \:\Big\{\:5\:\times \:Side\:\Big\}\:\:=\:\Big\{ \:4\:\times \:Side\:\Big\}\qquad \qquad\qquad$

$\dashrightarrow \sf \:\Big\{\:5\:\times \:Side\:\Big\}\:\:=\:\Big\{ \:4\:\times \:Side\:\Big\}$

$\qquad \dag\underline {\frak{ Substituting \:Known\:Values\:in\:Given \:Formula \:\::\:}}$

$\\\pmb{\frak{Where \:}}\:\begin{cases}\:\quad \sf Side_{\:(Square)}\:=\:\pmb{\frak{a\:cm}}\:\\\:\quad \sf Side_{\:(Pentagon)}\: \:=\:\pmb{\frak{ 5.6\:cm\:}}\:\end{cases}$

$\twoheadrightarrow \sf \:\Big\{\:5\:\times \:Side\:\Big\}\:\:=\:\Big\{ \:4\:\times \:Side\:\Big\} \\\\\\ \twoheadrightarrow \sf \:\Big\{\:5\:\times \:5.6\:\Big\}\:\:=\:\Big\{ \:4\:\times \:a\:\Big\} \\\\\\ \twoheadrightarrow \sf \:28\:\:= \:4a\: \\\\\\ \twoheadrightarrow \sf \:a\:\:= \:\cancel{\dfrac{28}{4}}\: \\\\\\\twoheadrightarrow \pmb {\underline {\boxed {\purple {\:\frak{ \:a\:\:=\:7\:cm\:}}}}}\:\bigstar \:$

$\therefore \underline {\sf Hence, \:Length \:of\:Side\:of\:Square \:is\:\pmb{\sf 7\:cm\:}\:.}$