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Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m. Find the dimensions of the garden.
Given :
Half the perimeter of a rectangular garden, whose length is 4 m more than its width, is 36 m.
To do:
We have to find the dimensions of the garden.
Solution :
Perimeter of a rectangle of length $l$ and breadth $b = 2 (l + b)$.
Let the length of the rectangle be $l$ and the width of the rectangle be $b$.
Therefore,
Half the perimeter of rectangle $=\frac{2\ ( l\ +\ b)}{2}$
Half the perimeter of rectangle $=l+b$.
Given that half the perimeter of the rectangular garden $= 36\ m$.
$l+b=36\ m$......(i)
It is given that, the length of the rectangular garden is 4 m more than its width.
This implies,
$l = b + 4$.......(ii)
Substituting (ii) in (i), we get,
$b + 4 + b = 36$
$2b = 36 - 4$
$2b = 32$
$b =\frac{32}{2}$
$b = 16\ m$
Substitute $b = 16$ in (ii)
$l = 16 + 4$
$l = 20\ m$
Therefore, the length of the rectangular garden is $20\ m$ and the width of the rectangular garden is $16\ m$.
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