To understand the relationship between the dimensions of the blackboard and the scale used in the drawing, let's first convert the dimensions of the blackboard from meters to inches.
The dimensions of the blackboard are:
- Width: \( \frac{9}{10} \) meters
- Height: \( \frac{7}{10} \) meters
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Convert meters to inches: There are 39.37 inches in a meter. Therefore, we'll convert the blackboard dimensions to inches using the conversion factor:
\[ \text{Width in inches} = \frac{9}{10} , \text{meters} \times 39.37 , \text{inches/meter} \] \[ \text{Width in inches} \approx 0.9 \times 39.37 \approx 35.433 , \text{inches} \]
\[ \text{Height in inches} = \frac{7}{10} , \text{meters} \times 39.37 , \text{inches/meter} \] \[ \text{Height in inches} \approx 0.7 \times 39.37 \approx 27.559 , \text{inches} \]
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Scale conversion from inches to meters: The drawing states that \( \frac{1}{2} \) of an inch represents 2 meters. Therefore, we can find out how many meters are represented by 1 inch:
\[ 1 , \text{inch} = 2 , \text{meters} \times 2 = 4 , \text{meters} \]
The scale is: \( 1 , \text{inch} \) represents \( 4 , \text{meters} \).
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Calculate the dimensions in the drawing: To find the size of the blackboard in the drawing, we can determine how many inches represent its actual dimensions:
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Width in the drawing: \[ \text{Width in the drawing} = \frac{\text{Actual Width}}{\text{Scale}} = \frac{35.433 , \text{inches}}{4 , \text{meters/inch}} = \frac{35.433}{4} \approx 8.858 , \text{inches} \]
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Height in the drawing: \[ \text{Height in the drawing} = \frac{\text{Actual Height}}{\text{Scale}} = \frac{27.559 , \text{inches}}{4} \approx 6.88975 , \text{inches} \]
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Therefore, in the drawing, the dimensions of the blackboard approximately are:
- Width: \( 8.86 , \text{inches} \)
- Height: \( 6.89 , \text{inches} \)
These calculations show how the actual dimensions of the blackboard can be represented on a scale drawing.