Use the image to answer the question.

A trapezoid shows the longest side measuring 6 feet and the opposite parallel side measuring 3 feet. The two legs measure 3 feet each.

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.

(1 point)
feet

1 answer

To solve this problem, we need to determine the lengths of the other sides of the trapezoidal table given that the greatest length (the longest side) of the trapezoid is represented by 1.5 feet in the scale drawing.

The original trapezoid has the following measurements:

  • Longest side (base 1) = 6 feet
  • Shortest side (base 2) = 3 feet
  • Two legs = 3 feet each

Let's find the lengths of the other sides when the longest side is scaled down to 1.5 feet.

Since the longest side (6 feet) in the original trapezoid corresponds to 1.5 feet in the scale drawing, we can find the scale factor:

\[ \text{Scale Factor} = \frac{\text{Length in scale drawing}}{\text{Original Length}} = \frac{1.5}{6} = 0.25 \]

Now, we apply this scale factor to the other dimensions of the trapezoid.

  1. For the opposite parallel side (3 feet): \[ \text{Scaled Length} = 3 \times 0.25 = 0.75 \text{ feet} \]

  2. For the legs (3 feet each): \[ \text{Scaled Length} = 3 \times 0.25 = 0.75 \text{ feet} \]

After applying the scale factor to all sides, we find:

  • Longest side: 1.5 feet
  • Shortest side: 0.75 feet
  • Two legs: 0.75 feet each

Therefore, the lengths of the other sides of the trapezoidal table in the scale drawing are 0.75 feet.

Thus, the final answer is:

0.75 feet.