Let's work through the given problem step-by-step to find the areas of the two possible rectangular floors for Nathan's toolshed and determine the larger area.
1. Identify the dimensions for each rectangle:
- The first set of dimensions is [tex]\( l_1 = 8 \)[/tex] units and [tex]\( w_1 = 6 \)[/tex] units.
- The second set of dimensions is [tex]\( l_2 = 7 \)[/tex] units and [tex]\( w_2 = 7 \)[/tex] units.
2. Calculate the area for the first set of dimensions:
- The area of a rectangle is given by the formula [tex]\( \text{Area} = l \times w \)[/tex].
- Substituting the values for the first set:
[tex]\[
\text{Area}_1 = l_1 \times w_1 = 8 \times 6 = 48 \text{ square units}
\][/tex]
3. Calculate the area for the second set of dimensions:
- Substituting the values for the second set:
[tex]\[
\text{Area}_2 = l_2 \times w_2 = 7 \times 7 = 49 \text{ square units}
\][/tex]
4. Compare the two areas:
- From our calculations, we have:
[tex]\[
\text{Area}_1 = 48 \text{ square units}
\][/tex]
[tex]\[
\text{Area}_2 = 49 \text{ square units}
\][/tex]
- The larger area between the two is [tex]\( 49 \text{ square units} \)[/tex].
Therefore, the area of the larger floor is [tex]\( 49 \text{ square units} \)[/tex].
The correct answer is:
[tex]\[
\boxed{49}
\][/tex]
