To determine whether Adoncia's scale drawing of the front of the Lincoln Memorial will fit on an [tex]\(8 \frac{1}{2}\)[/tex] in.-by-11 in. sheet of paper, let's go through the calculations step by step:
1. Understand the scale used in the drawing:
- The scale given is 15 feet in the monument to 1 inch in the drawing.
2. Convert the dimensions of the monument using the scale:
- The height of the monument is 80 feet.
- The length of the monument is 200 feet.
Using the scale:
- The height in the drawing: [tex]\(\frac{80 \text{ ft}}{15 \text{ ft/in}} = 5.3333 \text{ in}\)[/tex]
- The length in the drawing: [tex]\(\frac{200 \text{ ft}}{15 \text{ ft/in}} = 13.3333 \text{ in}\)[/tex]
3. Check if the drawing will fit on the paper:
- The height of the paper is [tex]\(8 \frac{1}{2} \text{ in} = 8.5 \text{ in}\)[/tex].
- The length of the paper is 11 inches.
Now we check if the scaled dimensions fit within these paper dimensions:
- Compare the drawing height (5.3333 in) to the paper height (8.5 in):
[tex]\(5.3333 \text{ in} \leq 8.5 \text{ in}\)[/tex] : True
- Compare the drawing length (13.3333 in) to the paper length (11 in):
[tex]\(13.3333 \text{ in} \leq 11 \text{ in}\)[/tex] : False
4. Conclusion:
- Although the height of the drawing (5.3333 inches) will fit within the height of the paper (8.5 inches), the length of the drawing (13.3333 inches) exceeds the length of the paper (11 inches).
Therefore, Adoncia's scale drawing of the front of the Lincoln Memorial will not fit on an [tex]\(8 \frac{1}{2}\)[/tex] in.-by-11 in. sheet of paper because it is too long.
