Question

the length of of a rectangular Garden is two times its breadth if the perimeter of the garden is 72cm find the length and breadth of the garden ​

Answer 1

Given :

• Length of a rectangle is two times its breadth .
• Perimeter of the Triangle is 72 cm

To Find :

• Length and Breadth = ?

SolutioN :

~ Formula Used :

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

Here :

• Length = 2y
• Breadth = y

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~ Calculating the Value of y :

${\dashrightarrow{\qquad{\sf{ Perimeter = 2 \bigg(Length + Breadth \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 72 = 2 \bigg(2y + y \bigg) }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 72 = 2 \times 3y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ 72 = 6y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \dfrac{72}{6} = y }}}} \\ \\ \\ \ {\dashrightarrow{\qquad{\sf{ \cancel\dfrac{72}{6} = y }}}} \\ \\ \\ \ {\qquad \; \; {\therefore \; {\underline{\boxed{\red{\pmb{\frak{ y = 12 }}}}}}}}$

$\\ \qquad{\rule{150pt}{1pt}}$

~ Calculating the Dimensions :

• Length = 2y = 2(12) = 24 cm
• Breadth = y = 12 cm

$\\ \qquad{\rule{150pt}{1pt}}$

~ Therefore :

❛❛ Length of the Rectangle is 24 cm and its breadth is 12 cm . ❜❜

$\\ {\underline{\rule{300pt}{9pt}}}$

Answer 2

$\underline{\underline{\large\bf{Given:-}}}$

• $\textsf{Perimeter of rectangular garden}$$\sf = 72\;cm$

$\underline{\underline{\large\bf{Assumptions:-}}}$

• $\textsf{let the length of rectangle }$$\sf= x$

$\red{\therefore}\:$$\textsf{Breadth of rectangular garden }$$\sf =2x$

$\quad\quad\quad \sf (Since \:length \: is \:two \:times)$

$\underline{\underline{\large\bf{To\: Find:-}}}$

• $\textsf{Length of the rectangular garden}$$\sf$
• $\textsf{Breadth of the rectangular garden}$$\sf$

$\underline{\underline{\large\bf{Solution:-}}}$

$\underline{\tt{Formula\:Applied}}$

$\green{ \underline { \boxed{ \sf{Perimeter\;of\: the\:garden= 2\times (l+b)}}}}$

where

• l = length
• b = breadth

$\underline{\tt\pink{Putting \:Values-}}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf Perimeter\;of\: the\:garden= 2\times (l+b) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 72 = 2\times (x+2x) \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 72 = 2\times 3x \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf 72 = 6x \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad \sf \frac{\cancel{72}}{\cancel{6}} = x \\\end{gathered}$

$\begin{gathered}\\\quad\longrightarrow\quad\boxed{ {\sf x = 12 cm}} \\\end{gathered}$

$\large{\red\bull}\; \sf length \:of\: rectangle = x$

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad\sf = 12\:cm$

$\large{\green\bull}\; \sf breadth \:of\: rectangle = 2x$

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad\sf =2\times 12\:cm$

$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad$$\quad\sf =24 \;cm$