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.
Step-by-Step Solution
Key Concept: Translate the word problem into a pair of linear equations in two variables (width and length) and solve them using substitution or elimination.
1. Let the width of the garden be $w$ metres.
2. Since the length is 4 m more than the width, let the length be $l = w + 4$ metres.
3. Perimeter of a rectangle = $2(l + w)$. Half of the perimeter is therefore $\frac{1}{2}\times 2(l + w) = l + w$.
4. According to the statement, half the perimeter equals 36 m, so
$$l + w = 36.$$
5. Substitute $l = w + 4$ into the above equation:
$$(w + 4) + w = 36$$
$$2w + 4 = 36$$
6. Solve for $w$:
$$2w = 36 - 4 = 32$$
$$w = \frac{32}{2} = 16 \text{ m}$$
7. Find the length using $l = w + 4$:
$$l = 16 + 4 = 20 \text{ m}$$
8. Hence, the dimensions of the garden are:
- Width = 16 m
- Length = 20 m
Correct Answer: Width = 16 m, Length = 20 m