Half the perimeter of a 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 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, 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 $16\ m$.