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Answer :
- Calculate the billboard's width in inches: $144 \times 4 = 576$ inches.
- Calculate the billboard's length in inches: $42 \times 4 = 168$ inches.
- Convert the width to feet: $\frac{576}{12} = 48$ feet, and the length to feet: $\frac{168}{12} = 14$ feet.
- Calculate the area in square feet: $48 \times 14 = 672$ square feet. The dimensions of the billboard are 48 feet wide and 14 feet long, and the area is $\boxed{672}$ square feet.
### Explanation
1. Find the dimensions in inches
The advertisement is 144 inches wide and 42 inches long. We want to create a billboard using a scale factor of 4. First, we need to find the dimensions of the billboard in inches.
2. Calculate the width and length in inches
To find the width of the billboard in inches, we multiply the width of the advertisement by the scale factor: $$144 \, \text{inches} \times 4 = 576 \, \text{inches}$$
To find the length of the billboard in inches, we multiply the length of the advertisement by the scale factor: $$42 \, \text{inches} \times 4 = 168 \, \text{inches}$$
3. Convert inches to feet
Now, we need to convert the dimensions from inches to feet. Since there are 12 inches in a foot, we divide the dimensions in inches by 12 to get the dimensions in feet.
Billboard Width: $$\frac{576 \, \text{inches}}{12 \, \text{inches/foot}} = 48 \, \text{feet}$$
Billboard Length: $$\frac{168 \, \text{inches}}{12 \, \text{inches/foot}} = 14 \, \text{feet}$$
4. Calculate the area in square feet
So, the dimensions of the billboard are 48 feet wide and 14 feet long. Now we need to find the area of the billboard in square feet. To do this, we multiply the width and length in feet:$$48 \, \text{feet} \times 14 \, \text{feet} = 672 \, \text{square feet}$$
5. State the final answer
Therefore, the dimensions of the billboard are 48 feet wide and 14 feet long, and the area of the billboard is 672 square feet.
### Examples
Scale factors are used in many real-world applications, such as mapmaking, architectural design, and creating models. For example, an architect uses a scale factor to create a blueprint of a building, where every dimension is proportionally smaller than the actual building. This allows them to visualize and plan the construction on a manageable scale. Similarly, mapmakers use scale factors to represent large geographical areas on a smaller map, making it easier to navigate and understand distances.
- Calculate the billboard's length in inches: $42 \times 4 = 168$ inches.
- Convert the width to feet: $\frac{576}{12} = 48$ feet, and the length to feet: $\frac{168}{12} = 14$ feet.
- Calculate the area in square feet: $48 \times 14 = 672$ square feet. The dimensions of the billboard are 48 feet wide and 14 feet long, and the area is $\boxed{672}$ square feet.
### Explanation
1. Find the dimensions in inches
The advertisement is 144 inches wide and 42 inches long. We want to create a billboard using a scale factor of 4. First, we need to find the dimensions of the billboard in inches.
2. Calculate the width and length in inches
To find the width of the billboard in inches, we multiply the width of the advertisement by the scale factor: $$144 \, \text{inches} \times 4 = 576 \, \text{inches}$$
To find the length of the billboard in inches, we multiply the length of the advertisement by the scale factor: $$42 \, \text{inches} \times 4 = 168 \, \text{inches}$$
3. Convert inches to feet
Now, we need to convert the dimensions from inches to feet. Since there are 12 inches in a foot, we divide the dimensions in inches by 12 to get the dimensions in feet.
Billboard Width: $$\frac{576 \, \text{inches}}{12 \, \text{inches/foot}} = 48 \, \text{feet}$$
Billboard Length: $$\frac{168 \, \text{inches}}{12 \, \text{inches/foot}} = 14 \, \text{feet}$$
4. Calculate the area in square feet
So, the dimensions of the billboard are 48 feet wide and 14 feet long. Now we need to find the area of the billboard in square feet. To do this, we multiply the width and length in feet:$$48 \, \text{feet} \times 14 \, \text{feet} = 672 \, \text{square feet}$$
5. State the final answer
Therefore, the dimensions of the billboard are 48 feet wide and 14 feet long, and the area of the billboard is 672 square feet.
### Examples
Scale factors are used in many real-world applications, such as mapmaking, architectural design, and creating models. For example, an architect uses a scale factor to create a blueprint of a building, where every dimension is proportionally smaller than the actual building. This allows them to visualize and plan the construction on a manageable scale. Similarly, mapmakers use scale factors to represent large geographical areas on a smaller map, making it easier to navigate and understand distances.
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