Question

zoe is taking the measurements of her lawn. her lawn is 64.15 feet long and 22.70 meters wide. one foot is equivalent to 0.3048 meters. which dimension of zoes lawn is longer, and how many yards longer is it?
a. the length of the lawn is 3.15 yards longer than the width.
b. the length of the lawn is 6.52 yards longer than the width.
c. the width of the lawn is 3.44 yards longer than the length.
d. the width of the lawn is 10.33 yards longer than the length.

Explanation:

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<reasoning>

Convert the length to meters

Using the Unit Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} L_{\text{meters}} &= 64.15\text{ feet} \times 0.3048\text{ meters/foot} \\ L_{\text{meters}} &\approx 19.55292\text{ meters} \end{aligned}$$

\]

Compare the dimensions

Using the Relative Comparison knowledge point
\[

$$\begin{aligned} W_{\text{meters}} &= 22.70\text{ meters} \\ L_{\text{meters}} &\approx 19.55\text{ meters} \\ W_{\text{meters}} &> L_{\text{meters}} \end{aligned}$$

\]
The width is longer than the length.

Calculate the difference in meters

Using the Relative Comparison knowledge point
\[

$$\begin{aligned} \Delta_{\text{meters}} &= 22.70\text{ meters} - 19.55292\text{ meters} \\ \Delta_{\text{meters}} &\approx 3.14708\text{ meters} \end{aligned}$$

\]

Convert the difference to yards

Using the Unit Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} \Delta_{\text{feet}} &= \frac{3.14708\text{ meters}}{0.3048\text{ meters/foot}} \approx 10.32507\text{ feet} \\ \Delta_{\text{yards}} &= \frac{10.32507\text{ feet}}{3\text{ feet/yard}} \approx 3.44169\text{ yards} \end{aligned}$$

\]
The width of the lawn is approximately \(3.44\) yards longer than the length.
</reasoning>

<answer>
<mcq-option>a. The length of the lawn is 3.15 yards longer than the width.</mcq-option>
<mcq-option>b. The length of the lawn is 6.52 yards longer than the width.</mcq-option>
<mcq-correct>c. The width of the lawn is 3.44 yards longer than the length.</mcq-correct>
<mcq-option>d. The width of the lawn is 10.33 yards longer than the length.</mcq-option>
</answer>

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Answer:

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<reasoning>

Convert the length to meters

Using the Unit Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} L_{\text{meters}} &= 64.15\text{ feet} \times 0.3048\text{ meters/foot} \\ L_{\text{meters}} &\approx 19.55292\text{ meters} \end{aligned}$$

\]

Compare the dimensions

Using the Relative Comparison knowledge point
\[

$$\begin{aligned} W_{\text{meters}} &= 22.70\text{ meters} \\ L_{\text{meters}} &\approx 19.55\text{ meters} \\ W_{\text{meters}} &> L_{\text{meters}} \end{aligned}$$

\]
The width is longer than the length.

Calculate the difference in meters

Using the Relative Comparison knowledge point
\[

$$\begin{aligned} \Delta_{\text{meters}} &= 22.70\text{ meters} - 19.55292\text{ meters} \\ \Delta_{\text{meters}} &\approx 3.14708\text{ meters} \end{aligned}$$

\]

Convert the difference to yards

Using the Unit Conversion and Dimensional Analysis knowledge points
\[

$$\begin{aligned} \Delta_{\text{feet}} &= \frac{3.14708\text{ meters}}{0.3048\text{ meters/foot}} \approx 10.32507\text{ feet} \\ \Delta_{\text{yards}} &= \frac{10.32507\text{ feet}}{3\text{ feet/yard}} \approx 3.44169\text{ yards} \end{aligned}$$

\]
The width of the lawn is approximately \(3.44\) yards longer than the length.
</reasoning>

<answer>
<mcq-option>a. The length of the lawn is 3.15 yards longer than the width.</mcq-option>
<mcq-option>b. The length of the lawn is 6.52 yards longer than the width.</mcq-option>
<mcq-correct>c. The width of the lawn is 3.44 yards longer than the length.</mcq-correct>
<mcq-option>d. The width of the lawn is 10.33 yards longer than the length.</mcq-option>
</answer>

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