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Answer :
To find the actual height of a mastil drawn on a scale, follow these steps:
1. Understand the Scale:
The tree is 42 feet tall in real life and is drawn to a height of 6 inches. This provides the scale of the drawing.
2. Find the Scale Factor:
To determine how many feet in real life each inch on the drawing represents, divide the actual height of the tree by its height in the drawing:
[tex]\[
\text{Scale factor} = \frac{\text{Actual height of the tree}}{\text{Height of the tree in the drawing}} = \frac{42 \text{ feet}}{6 \text{ inches}}
\][/tex]
3. Calculate the Scale Factor:
Simplifying [tex]\(\frac{42}{6}\)[/tex] gives us a scale factor of 7 feet per inch.
4. Calculate the Actual Height of the Mastil:
Since the mastil is drawn at a height of 7 inches, use the scale factor to find its actual height:
[tex]\[
\text{Actual height of the mastil} = \text{Height of the mastil in the drawing} \times \text{Scale factor} = 7 \text{ inches} \times 7 \text{ feet/inch}
\][/tex]
5. Final Calculation:
Multiply 7 by 7 to get:
[tex]\[
7 \times 7 = 49 \text{ feet}
\][/tex]
The actual height of the mastil is 49 feet.
1. Understand the Scale:
The tree is 42 feet tall in real life and is drawn to a height of 6 inches. This provides the scale of the drawing.
2. Find the Scale Factor:
To determine how many feet in real life each inch on the drawing represents, divide the actual height of the tree by its height in the drawing:
[tex]\[
\text{Scale factor} = \frac{\text{Actual height of the tree}}{\text{Height of the tree in the drawing}} = \frac{42 \text{ feet}}{6 \text{ inches}}
\][/tex]
3. Calculate the Scale Factor:
Simplifying [tex]\(\frac{42}{6}\)[/tex] gives us a scale factor of 7 feet per inch.
4. Calculate the Actual Height of the Mastil:
Since the mastil is drawn at a height of 7 inches, use the scale factor to find its actual height:
[tex]\[
\text{Actual height of the mastil} = \text{Height of the mastil in the drawing} \times \text{Scale factor} = 7 \text{ inches} \times 7 \text{ feet/inch}
\][/tex]
5. Final Calculation:
Multiply 7 by 7 to get:
[tex]\[
7 \times 7 = 49 \text{ feet}
\][/tex]
The actual height of the mastil is 49 feet.
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