To find the area of the actual bridge deck in square feet, we'll need to follow a series of steps, converting the scaled dimensions to actual dimensions and then calculating the area.
1. Scale Factor: The scale factor is 40:1. This means that every inch in the scaled drawing represents 40 inches in the actual bridge deck.
2. Scaled Dimensions: The dimensions of the scaled bridge deck are given as 42 inches in length and [tex]\(4 \frac{4}{5}\)[/tex] inches in width.
3. Convert Width to a Mixed Number:
- The width of [tex]\(4 \frac{4}{5}\)[/tex] inches can be converted to an improper fraction as:
[tex]\[
4 \frac{4}{5} = 4 + \frac{4}{5} = \frac{20}{5} + \frac{4}{5} = \frac{24}{5}
\][/tex]
- Converting the improper fraction to a decimal:
[tex]\[
\frac{24}{5} = 4.8 \text{ inches}
\][/tex]
4. Scale Up Dimensions:
- Length of the actual bridge deck:
[tex]\[
42 \text{ inches} \times 40 = 1680 \text{ inches}
\][/tex]
- Width of the actual bridge deck:
[tex]\[
4.8 \text{ inches} \times 40 = 192 \text{ inches}
\][/tex]
5. Convert Inches to Feet:
- 1 foot = 12 inches, so:
- Length in feet:
[tex]\[
\frac{1680 \text{ inches}}{12} = 140 \text{ feet}
\][/tex]
- Width in feet:
[tex]\[
\frac{192 \text{ inches}}{12} = 16 \text{ feet}
\][/tex]
6. Calculate Area:
- The area of a rectangle is given by:
[tex]\[
\text{Area} = \text{length} \times \text{width}
\][/tex]
- Substituting the actual dimensions in feet:
[tex]\[
\text{Area} = 140 \text{ feet} \times 16 \text{ feet} = 2240 \text{ square feet}
\][/tex]
Therefore, the area of the actual bridge deck is [tex]\(2240\)[/tex] square feet.
The correct option is [tex]\(2240\)[/tex] square feet.
