To solve for the lengths of the sides of the trapezoidal table represented on the scale drawing, we will first summarize the dimensions provided in the context of a trapezoid orientation.
We have:
- Top side (shorter base) = 3 ft
- Right side = 3 ft
- Bottom side (longer base) = 3 ft
- Left side = 6 ft
From the description:
- The trapezoid is vertical, suggesting the orientation is such that the 3 ft length on top and bottom are horizontal measurements.
- The shape of this trapezoid is effectively an isosceles trapezoid given that both the top and bottom sides measure 3 ft, while the left side is taller.
Given that the greatest length of the table in the scale drawing is represented by 1.5 feet, we assume this corresponds to the longer base of the original trapezoid.
To find the scale factor, we can use the bottom side (longer base) of the trapezoid.
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Identify the actual length of the bottom side: 3 ft (from the problem statement).
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Calculate the scale factor: \[ \text{Scale factor} = \frac{\text{Length in drawing}}{\text{Actual length}} = \frac{1.5 \text{ ft}}{3 \text{ ft}} = 0.5 \]
Next, we will apply this scale factor to the remaining sides of the trapezoid.
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Top side (3 ft): \[ 3 \text{ ft} \times 0.5 = 1.5 \text{ ft} \]
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Right side (3 ft): \[ 3 \text{ ft} \times 0.5 = 1.5 \text{ ft} \]
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Bottom side (3 ft): \[ 3 \text{ ft} \times 0.5 = 1.5 \text{ ft} \]
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Left side (6 ft): \[ 6 \text{ ft} \times 0.5 = 3 \text{ ft} \]
So, in total from the scale drawing, the lengths of the sides of the trapezoidal table are:
- Top side: 1.5 ft
- Right side: 1.5 ft
- Bottom side: 1.5 ft
- Left side: 3.0 ft
Thus, in decimal form, the lengths of the other sides of the table are:
1.5, 1.5, 1.5, 3.0