Question

Half the perimeter of a rectangular garden, whose length is 4 m more than its width is 36m. Then find the dimensions of the garden.

Answer 1

Hint: In this particular type of question express the width and length as x and x+4 respectively using the information given in the question. Now we have to use the formula of perimeter of a rectangle and equate to find the desired quantities.

Complete step-by-step answer:
Let the width of the garden be x .
Then length of the garden = $x + 4$
Perimeter = $2\left( {length + breadth} \right)$
$\dfrac{1}{2}Perimeter = \dfrac{1}{2} \times 2 \times \left( {length + breadth} \right) = length + breadth$
But $\dfrac{1}{2}perimeter = 36m$ ( given )
$ \Rightarrow length + breadth = 36m$
$ \Rightarrow \left( {x + 4} \right) + x = 36$
$ \Rightarrow 2x + 4 = 36 \Rightarrow 2x = 32 \Rightarrow x = 16m$
Therefore Length of the garden = x+4 = 16+4 = 20m
Breadth of the garden = x = 16m

Note: Remember to recall the formula of the perimeter of a rectangle to solve such types of questions. Formation of equations must be proper and the solution should be in a systematic manner to avoid confusion and provide accuracy.