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.
Let the length of the rectangular garden be \(l\) metres and the width be \(b\) metres.
Given that the length is 4 m more than the width:
\[ l = b + 4. \]
Perimeter of a rectangle is \(2(l + b)\). Half the perimeter is therefore \(l + b\).
It is given that half the perimeter is 36 m:
\[ l + b = 36. \]
So we have the system
\[ l = b + 4, \qquad l + b = 36. \]
Substitute \(l = b + 4\) in \(l + b = 36\):
\[ (b + 4) + b = 36 \Rightarrow 2b + 4 = 36 \Rightarrow 2b = 32 \Rightarrow b = 16. \]
Then
\[ l = b + 4 = 16 + 4 = 20. \]
Therefore, the dimensions of the garden are: length \(20\) m and breadth \(16\) m.
Translate the wording into two equations: one from “length is 4 m more” and one from the given half-perimeter. Substitute the first into the second to solve for width, then back-solve for length.