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Michael made a scale drawing of a game room. The pool table is 6 inches wide in the drawing. The actual pool table is 3 feet wide. What scale factor does the drawing use? Simplify your answer and write it as a fraction.

Ask by Cross Lee. in the United States
Mar 14,2025

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Answer

The scale factor is \(\frac{1}{6}\).

Solution

To find the scale factor of the drawing, we need to compare the width of the pool table in the drawing to the actual width of the pool table. 1. **Convert the actual width to the same unit as the drawing:** - The actual width of the pool table is 3 feet. Since there are 12 inches in a foot, we convert feet to inches: \[ 3 \text{ feet} = 3 \times 12 \text{ inches} = 36 \text{ inches} \] 2. **Set up the scale factor:** - The scale factor is the ratio of the width in the drawing to the actual width: \[ \text{Scale Factor} = \frac{\text{Width in Drawing}}{\text{Actual Width}} = \frac{6 \text{ inches}}{36 \text{ inches}} \] 3. **Simplify the fraction:** - We can simplify \(\frac{6}{36}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 6: \[ \frac{6 \div 6}{36 \div 6} = \frac{1}{6} \] Thus, the scale factor used in the drawing is \(\frac{1}{6}\).

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Bonus Knowledge

To find the scale factor, we need to compare the width of the pool table in the drawing to its actual width. The drawing shows the pool table as 6 inches wide, while the actual table is 3 feet wide. First, we need to convert 3 feet to inches: 3 feet × 12 inches/foot = 36 inches. Now, we calculate the scale factor as the drawing width divided by the actual width. Scale factor = Drawing width / Actual width = 6 inches / 36 inches = 1/6. So, the scale factor used in the drawing is 1/6.

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