Question

Half of the perimeter of a rectangular garden is 36 m . If Length of
the garden is 4 m more than its width then find the dimensions of
garden

Answer 1

Given that half of the perimeter of a rectangular garden is 36 m, we can set up the following equation for the perimeter \( P \):

\[
P = 2 \times 36 = 72 \text{ m}
\]

The formula for the perimeter of a rectangle is:

\[
P = 2 \times (\text{Length} + \text{Width})
\]

Let the width of the garden be \( w \) meters. According to the problem, the length \( l \) of the garden is 4 meters more than the width:

\[
l = w + 4
\]

Substituting the expression for the length into the perimeter formula:

\[
72 = 2 \times (w + (w + 4))
\]

Simplifying the equation:

\[
72 = 2 \times (2w + 4)
\]
\[
72 = 4w + 8
\]

Now, let's isolate \( w \):

\[
72 - 8 = 4w
\]
\[
64 = 4w
\]
\[
w = \frac{64}{4} = 16 \text{ m}
\]

Now substituting \( w = 16 \) back into the equation for the length:

\[
l = w + 4 = 16 + 4 = 20 \text{ m}
\]

Thus, the dimensions of the garden are:

- Width: \( 16 \text{ m} \)
- Length: \( 20 \text{ m} \)

Final answer:
- Length = 20 m
- Width = 16 m