Question

A piece of wire in form of a circle has a radius of 28cm .it is reshaping into a rectangle of 50cm length. Calculate the width of the rectangle

Answer 1

$Radius \:of \:a \:circular \:wire (r) = 28\:cm$

/*After reshaping it into a rectangle */

$Length (l) = 50\:cm$

$Let \:width = w$

$Perimeter_{\pink{(rectangle)}}= Circumfernce_{\blue{(rectangle)}}$

$\implies 2(l+w) = 2\pi r$

$\implies l+w = \pi r$

$\implies 50 + w = \frac{22}{7} \times 28$

$\implies 50 + w = 22\times 4$

$\implies w = 88 - 50$

$\implies w = 38 \:cm$

Therefore.,

$\red{Width \:of \:the \:rectangle } \green{=38 \:cm}$

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Answer 2

$\bf{\underline{\underline{\bigstar\bigstar\: Given : }}}$

$\:\:$

• $\footnotesize{ Radius \: of \: wire (r) = 28cm}$

• $\footnotesize{ Length \: of \: rectangle (l) = 50cm}$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: To \: Find : }}}$

$\:\:$

• $\footnotesize{ width \: of \: rectangle( b )}$

$\:\:$

$\bf{\underline{\underline{\bigstar\bigstar\: Solution :}}}$

$\:\:$

$\footnotesize{ {circumference}_{circle} = {perimeter}_{rectangle}}$

$\footnotesize{ 2 \pi r = 2(l + b) }$

$\footnotesize{ 2 \times \dfrac{22}{7} \times 28cm = 2(50cm + b) }$

$\footnotesize{ 2 \times 22 \times 4cm = 2(50cm + b) }$

$\footnotesize{ 2 \times 88cm = 2(50cm + b) }$

$\footnotesize{ 176cm = 2(50cm + b) }$

$\footnotesize{ \dfrac{176cm}{2} = 50cm + b }$

$\footnotesize{ 88cm = 50cm + b }$

$\footnotesize{ 88cm - 50cm = b }$

$\footnotesize{ 38cm = b }$

$\:\:$

$\bold{\underline{\bigstar \:38cm\: is\: width \: of \: rectangle}}$