The image shows a table at a restaurant in the shape of a trapezoid. The restaurant owners want to determine if trapezoidal tables will fit comfortably into the rest of the dining room. The owners make a scale drawing of the dining room and a scale drawing of the table. If the greatest length of the table is represented in the scale drawing by 1.5 feet, what will the length of the other sides of the table be? Write your answer in decimal form.

The trapezoid is vertical. At the top there is the measurement 3ft. On the right side (smaller base) there is also a 3ft measurement. On the bottom its also a 3ft measurement. On the left side (longer base) there is a 6ft measurement.

1 answer

To determine the lengths of the other sides of the trapezoidal table based on the scale drawing, we first need to understand the situation described.

We have a trapezoid where:

  • The top base (shorter side) measures 3 feet.
  • The bottom base (longer side) measures 6 feet.
  • The left side height is 3 feet.
  • The right side (of the shorter base) is also 3 feet.

According to the information, the greatest length (which seems to refer to the longer base of the trapezoid) is represented by 1.5 feet in the scale drawing.

To find the scale factor, we can compare the real length of the longer base (6 feet) with its scale representation (1.5 feet): \[ \text{Scale Factor} = \frac{\text{Actual Length}}{\text{Scale Length}} = \frac{6 \text{ ft}}{1.5 \text{ ft}} = 4. \]

Now, knowing the scale factor, we can find the lengths of the other sides in the scale drawing:

  1. Length of the top base (3 ft in reality): \[ \text{Scale Length} = \frac{3 \text{ ft}}{4} = 0.75 \text{ ft (or 9 inches)}. \]

  2. Length of the left side (3 ft in reality): \[ \text{Scale Length} = \frac{3 \text{ ft}}{4} = 0.75 \text{ ft (or 9 inches)}. \]

  3. Length of the right side (3 ft in reality): \[ \text{Scale Length} = \frac{3 \text{ ft}}{4} = 0.75 \text{ ft (or 9 inches)}. \]

Thus, the lengths of the other sides of the trapezoidal table, represented in the scale drawing, are as follows:

  • Length of the top base: 0.75 ft
  • Length of the left side: 0.75 ft
  • Length of the right side: 0.75 ft

Therefore, the answer in decimal form for the lengths of the other sides is:

0.75 ft for each of the shorter sides (top, left, and right).