Certainly! Let's solve this step-by-step.
1. Understand the problem:
- We are given the area of the rectangular plot: [tex]\(6 \frac{2}{5}\)[/tex] square meters.
- We are asked to find the length of the plot if the width is [tex]\(5 \frac{1}{7}\)[/tex] meters.
2. Convert the mixed numbers to improper fractions or decimals for ease of calculation:
- Convert [tex]\(6 \frac{2}{5}\)[/tex]:
[tex]\[
6 \frac{2}{5} = 6 + \frac{2}{5}
\][/tex]
Converting [tex]\(2/5\)[/tex] to a decimal:
[tex]\[
\frac{2}{5} = 0.4
\][/tex]
So,
[tex]\[
6 \frac{2}{5} = 6 + 0.4 = 6.4
\][/tex]
Thus, the area is [tex]\(6.4\)[/tex] square meters.
- Convert [tex]\(5 \frac{1}{7}\)[/tex]:
[tex]\[
5 \frac{1}{7} = 5 + \frac{1}{7}
\][/tex]
Converting [tex]\(1/7\)[/tex] to a decimal:
[tex]\[
\frac{1}{7} \approx 0.142857142857143
\][/tex]
So,
[tex]\[
5 \frac{1}{7} = 5 + 0.142857142857143 \approx 5.142857142857143
\][/tex]
Thus, the width is [tex]\(5.142857142857143\)[/tex] meters.
3. Use the area formula for a rectangle to find the length:
[tex]\[
\text{Area} = \text{Length} \times \text{Width}
\][/tex]
We need to solve for the length:
[tex]\[
\text{Length} = \frac{\text{Area}}{\text{Width}}
\][/tex]
Substituting the given values:
[tex]\[
\text{Length} = \frac{6.4}{5.142857142857143}
\][/tex]
Calculating the length:
[tex]\[
\text{Length} \approx 1.2444444444444445
\][/tex]
4. Conclusion:
- The area of the rectangular plot is [tex]\(6.4\)[/tex] square meters.
- The width of the plot is [tex]\(5.142857142857143\)[/tex] meters.
- Therefore, the length of the plot is approximately [tex]\(1.2444444444444445\)[/tex] meters.
Hence, the length of the rectangular plot is approximately [tex]\(1.244\)[/tex] meters.
