Question

The perimeter of a rectangular garden is 32 2/5 m. The length is twice the width. Find the length and the width of the rectangular garden (Estimate to the nearest tenths).
l = 5.1 m and w = 3.0 m
l = 10.8 m and w = 5.3 m
l = 5.2 m and w = 2.9 m
l = 10.8 m and w = 5.4 m

Answer 1

Given that the perimeter \(P\) of a rectangular garden is \(32 \frac{2}{5}\) m, we can first convert the mixed number into an improper fraction:

\[
32 \frac{2}{5} = \frac{32 \times 5 + 2}{5} = \frac{160 + 2}{5} = \frac{162}{5} \text{ m}
\]

The formula for the perimeter of a rectangle is:

\[
P = 2(l + w)
\]

where \(l\) is the length and \(w\) is the width. According to the problem, the length is twice the width:

\[
l = 2w
\]

Substituting \(l\) into the perimeter formula gives:

\[
\frac{162}{5} = 2(2w + w) = 2(3w) = 6w
\]

To find \(w\), we can rearrange the equation:

\[
6w = \frac{162}{5}
\]
\[
w = \frac{162}{5 \times 6} = \frac{162}{30} = \frac{27}{5} \approx 5.4 \text{ m} \quad (\text{for } w)
\]

Now substituting \(w\) back to find \(l\):

\[
l = 2w = 2 \times \frac{27}{5} = \frac{54}{5} \approx 10.8 \text{ m} \quad (\text{for } l)
\]

Thus, we find:

\[
l \approx 10.8 \text{ m} \quad \text{and} \quad w \approx 5.4 \text{ m}
\]

After estimating to the nearest tenth, the dimensions of the rectangular garden are:

\[
l = 10.8 \text{ m} \quad \text{and} \quad w = 5.4 \text{ m}
\]

So, the correct choice is:

**l = 10.8 m and w = 5.4 m.**