Question

Half the perimeter of a rectangular garden whose length is 6 m more than its width is 36 m , The dimensions of the garden are 
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Answer 1

Given:

• Length of rectanglular garden is 6 m more than its breadth.
• Half of perimeter of the rectanglular garden is 36 m.

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To find:

• Dimensions of garden?

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Solution:

Let Breadth of rectanglular garden be x m

Then, Length of rectanglular garden is (x + 6) m

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$\setlength{\unitlength}{1cm}\begin{picture}(0,0)\thicklines\multiput(0,0)(5,0){2}{\line(0,1){3}}\multiput(0,0)(0,3){2}{\line(1,0){5}}\put(0.03,0.02){\framebox(0.25,0.25)}\put(0.03,2.75){\framebox(0.25,0.25)}\put(4.74,2.75){\framebox(0.25,0.25)}\put(4.74,0.02){\framebox(0.25,0.25)}\multiput(2.1,-0.7)(0,4.2){2}{\sf\large (x + 6) m}\multiput(-1.4,1.4)(6.8,0){2}{\sf\large x m}\put(-0.5,-0.4){\bf A}\put(-0.5,3.2){\bf D}\put(5.3,-0.4){\bf B}\put(5.3,3.2){\bf C}\end{picture}$

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We know that,

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$\star\;{\boxed{\sf{\purple{Perimeter_{\;(rectangle)} = 2(l + b)}}}}$

$\underline{\sf{\bigstar\; According\;to\;the\; Question\;:}}$

Half of perimeter of the rectanglular garden is 36 m

$:\implies\sf \dfrac{2(l + b)}{2} = 36$

$:\implies\sf l + b = 36$

Here,

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• Length, l = x m
• Breadth, b = (x + 6) m

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$:\implies\sf x + (x + 6) = 36$

$:\implies\sf 2x + 6 = 36$

$:\implies\sf 2x = 36 - 6$

$:\implies\sf 2x = 30$

$:\implies\sf x = \cancel{ \dfrac{30}{2}}$

$:\implies{\boxed{\sf{\pink{x = 15}}}}\;\bigstar$

Therefore,

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• Breadth of rectanglular garden, x = 15 m
• Length of rectanglular garden, (x + 6) = 21 m

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$\therefore\;{\underline{\sf{Hence,\; Dimensions\;of\;rectangular\;garden\;is\;21\;m\;and\;15\;m\: respectively.}}}$

Answer 2

Given ,

• The half of the perimeter of rectangle is 36 m

• The length of rectangle is 6 m more than its width

∴Perimeter of rectangle = 2 × 36 i.e 72 m

Let , the breadth of rectangle be " x "

Then , length = " x + 6 "

We know that , the perimeter of rectangle is given by

$\boxed{ \tt{Perimeter = 2(length + breadth)}}$

Thus ,

72 = 2(x + 6 + x)

36 = 2x + 6

30 = 2x

x = 30/2

x = 15 m

Therefore , the length and breadth of rectangle are 21 m and 15 m

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