Question

Q. The perimeter of a rectangle is 240 cm if the breadth of the rectangle is 30 cm find its length also find the area of rectangle​

Answer 1

${\huge{\underline{\bf{AnsWer :}}}}$

Perimeter of the rectangle = 240 cm

Breadth = 30cm

Length = ??

We know that,

Perimeter of a rectangle = 2(l + b)

=> 240 = 2(l + 30)

=> 240/2 = l + 30

=> 120 = l + 30

=> l = 120-30

=> l = 90cm.

Hence, we got length as 90cm

Area of the rectangle = l*b

= 90*30

= 2700cm² ans.

Answer 2

$\begin{gathered}\sf Given \begin{cases} & \sf{Perimeter\:of\:rectangle = \bf{240\:cm}} \\ & \sf{Breadth\:of\:rectangle = \bf{30\:cm}} \end{cases}\\ \\\end{gathered}$

• To find: Length & Area of rectangle?

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• ☯ Let length of rectangle be x cm.

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$\begin{gathered}\underline{\bigstar\:\boldsymbol{According\:to\:the\:question\::}}\\ \\\end{gathered}$

• The perimeter of a rectangle is 240 cm.

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$\begin{gathered}\dag\;{\underline{\frak{Perimeter\:of\:rectangle\:is\:given\:by,}}}\\ \\\end{gathered}$

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

$\begin{gathered}:\implies\sf 2(x + 30) = 240\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf x + 30 = \cancel{ \dfrac{240}{2}}\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf x + 30 = 120\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf x = 120 - 30\\ \\\end{gathered}$

$\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{x = 90\:cm}}}}}\;\bigstar\\ \\\end{gathered}$

$\therefore\:{\underline{\sf{Length\:of\:rectangle\:is\: {\textsf{\textbf{90\:cm}}}.}}}$

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$\begin{gathered}\dag\;{\underline{\frak{Now,\:Finding\:area\:of\:rectangle,}}}\\ \\\end{gathered}$

$\begin{gathered}\star\;{\boxed{\sf{\pink{Area_{\;(rectangle)} = length \times breadth}}}}\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf Area_{\;(rectangle)} = x \times 30\\ \\\end{gathered}$

$\begin{gathered}:\implies\sf Area_{\;(rectangle)} = 90 \times 30\\ \\\end{gathered}$

$\begin{gathered}:\implies{\underline{\boxed{\frak{\purple{Area_{\;(rectangle)} = 2700\:cm^2}}}}}\;\bigstar\\ \\\end{gathered}$

$\therefore\:{\underline{\sf{Hence,\:Area\:of\:rectangle\:is\: \bf{2700\:cm^2}.}}}$