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Nathan is building a toolshed with a rectangular floor. The area of a rectangle is given by the formula [tex] A = l \times w [/tex], where [tex] l [/tex] represents the length, and [tex] w [/tex] represents the width. The floor of the shed will have measurements of either [tex] l = 8 \, \text{and} \, w = 6 [/tex] or [tex] l = 7 \, \text{and} \, w = 7 [/tex].

What is the area of the larger floor?

A. 49
B. 42
C. 48

Sagot :

GinnyAnswer
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]
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