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Answer :
To find the scale used to represent the height of a building in a picture, you'll need to compare the actual height of the building to its height in the picture.
1. Determine the actual height in inches:
The building's actual height is given as 42 feet. Since 1 foot is equal to 12 inches, convert the height to inches:
[tex]\[
\text{Actual height in inches} = 42 \, \text{feet} \times 12 \, \text{inches per foot} = 504 \, \text{inches}
\][/tex]
2. Identify the picture height:
The building's height in the picture is given as 7 inches.
3. Calculate the scale ratio:
The scale is the ratio of the picture height to the actual height in the same units. So, the scale is calculated by dividing the picture height by the actual height in inches:
[tex]\[
\text{Scale} = \frac{\text{Picture height in inches}}{\text{Actual height in inches}} = \frac{7 \, \text{inches}}{504 \, \text{inches}}
\][/tex]
4. Simplify the scale:
The result of this division gives the scale of the picture to the actual height:
[tex]\[
\text{Scale} \approx 0.013888888888888888
\][/tex]
This scale essentially means that every inch on the picture corresponds to approximately 72 inches (or 6 feet) of the actual building’s height, as the actual height of 504 inches is shown as 7 inches in the picture.
1. Determine the actual height in inches:
The building's actual height is given as 42 feet. Since 1 foot is equal to 12 inches, convert the height to inches:
[tex]\[
\text{Actual height in inches} = 42 \, \text{feet} \times 12 \, \text{inches per foot} = 504 \, \text{inches}
\][/tex]
2. Identify the picture height:
The building's height in the picture is given as 7 inches.
3. Calculate the scale ratio:
The scale is the ratio of the picture height to the actual height in the same units. So, the scale is calculated by dividing the picture height by the actual height in inches:
[tex]\[
\text{Scale} = \frac{\text{Picture height in inches}}{\text{Actual height in inches}} = \frac{7 \, \text{inches}}{504 \, \text{inches}}
\][/tex]
4. Simplify the scale:
The result of this division gives the scale of the picture to the actual height:
[tex]\[
\text{Scale} \approx 0.013888888888888888
\][/tex]
This scale essentially means that every inch on the picture corresponds to approximately 72 inches (or 6 feet) of the actual building’s height, as the actual height of 504 inches is shown as 7 inches in the picture.
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