Question

The length of a rectangular field is 100 m. If the perimeter is 300 m, what is its breadth?
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Answer 1

$\bf Given\begin{cases} & \sf{Length\:of\;rectangular\;field = \bf{100\;m}} \\ & \sf{Perimeter\;of\;rectangular\;field = \bf{300\;m}} \end{cases}$

To find:

• Breadth of rectangular field?

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☯ Let breadth of rectangular field be x m.

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$\dag\;{\underline{\frak{As\;we\;know\;that,}}}$

$\star\;{\boxed{\sf{\pink{Perimeter_{\;(rectangle)} = 2(length + breadth)}}}}$

Therefore,

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${\underline{\sf{\bigstar\: According\:to\:the\:question\::}}}$

$:\implies\sf 2(100 + x) = 300$

$:\implies\sf (100 + x) = \cancel{\dfrac{300}{2}}$

$:\implies\sf 100 + x = 150$

$:\implies\sf x = 150 - 100$

$:\implies{\underline{\boxed{\sf{\purple{x = 50}}}}}\;\bigstar$

$\therefore\;{\underline{\sf{Breadth\:of\;rectangular\;field\;is\; {\textsf{\textbf{50\;m}}}.}}}$

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$\qquad\qquad\boxed{\bf{\mid{\overline{\underline{\pink{\bigstar\: More\:to\:know :}}}}}\mid}$

Area of rectangle = length × breadth

Diagonal of rectangle = √(length)² + (breadth)²

Area of square = side × side

Perimeter of square = 4 × side

Diagonal of square = √2 × side

Answer 2

$\huge{ \boxed{ \frak {Answer}}}$

$\large \underline{\underline {\frak{ \color{red}Given::}}}$

$: \mapsto \sf{Length \: of \: rectangle=100m}$

${: \mapsto \sf{Perimeter \: of \: rectangle=300m}}$

$\large \underline{\underline {\frak{ \color{blue}To \: find::}}}$

$\leadsto \sf{Breadth \: of \: rectangle.}$

$\large \underline{\underline {\frak{ \color{indigo}Formula \: required::}}}$

$\maltese{ \fbox{Perimeter \: of \: rectangle = 2( Length + Breadth)}} \maltese$

$\large \underline{\underline {\frak{ \color{ind}According \: to \: Question::}}}$

${: \implies{ \sf{Perimeter \: of \: rectangle = 2( Length + Breadth)}}}$

${: \implies{ \sf{300m = 2( 150m + Breadth)}}}$

${: \implies{ \sf{ \frac{300}{2}m = 100m + Breadth}}}$

${: \implies{ \sf{150m = 100m + Breadth}}}$

${: \implies{ \sf{Breadth = 150m - 100m}}}$

${: \implies{ \sf{Breadth = 50m}}}$

$\large \underline{\underline {\bf{ \color{cyan}Hence, }}}$

$\: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \star{\underline{ \fbox{ \sf{Breadth = 50m}}}}$

$\large \underline{\underline {\frak{ \color{peru}Learn \: more \: about \: rectangle::}}}$

${ \boxed{ \begin{gathered} \begin{array}{ |c|c| } \hline \sf Perimeter \: of \: rectangle & \sf2(length + breadth) \\ \hline \sf Area \: of \: rectangle& \sf length \times breadth \\ \hline \sf Length \: of \: rectangle& \sf\frac{Area}{Breadth} \\ \hline \sf Breadth \: of \: rectangle & \sf\frac{Area }{Length} \\ \end{array} \end{gathered}}}$