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Half the perimeter of a rectangular garden, whose length is 4m more than its width, is 36m. Find the dimensions of the garden.
A. Length is 30m and breadth is 15m.
B. Length is 20m and breadth is 16m.
C. Length is 40m and breadth is 30m.
D. Length is 45m and breadth is 18m.

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Last updated date: 17th Jul 2024
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Answer
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Hint: In this question, we will use the formula of the perimeter of a rectangle given as $2(l + b)$ . So, we will proceed further by assuming .


Complete step-by-step answer:

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Given statement is “Half the perimeter of a rectangular garden, whose length is 4m more than its width, is 36m”

Let the width of the garden $ = x{\text{ m}}$

Length of the garden will be \[ = (x + 4)m\]

It is given that half of the perimeter is 36m.

Therefore the perimeter of the garden is

$

   = 2 \times 36 \\

   = 72m \\

 $

The perimeter of the rectangular garden is given by

$

   \Rightarrow 2(l + b) \\

   \Rightarrow 2(x + 4 + x) = 72 \\

   \Rightarrow2x + 4 = 36 \\

   \Rightarrow 2x = 32 \\

   \Rightarrow x = 16m \\

$

Therefore the width of the garden is 16m. And the length of the garden is

\[

   = (x + 4)m \\

   = 20m \\

 \]

Hence, dimensions of the garden is $20 \times 16.$

Hence the correct option is “B”.


Note: In order to solve such types of questions, draw figures to solve the problem. Remember all the formulas of rectangle, cone, square etc. First step is to gather information given in the question and then apply the formula. In the above question we used the formula of perimeter of rectangle, similarly in other questions we may have to use the formula of area.