Use the image to answer the question.

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

Answer 1

To find the lengths of the sides of the trapezoidal table in the scale drawing, we first need to determine the scale factor used in the drawings.

The actual longest side (6 feet) is represented as 1.5 feet in the scale drawing. To find the scale factor, we can set up the following ratio:

\[ \text{Scale Factor} = \frac{\text{Drawing Length}}{\text{Actual Length}} = \frac{1.5 \text{ feet}}{6 \text{ feet}} = \frac{1.5}{6} = \frac{1}{4} \]

Now, we will apply this scale factor to the other sides of the trapezoid in the actual dimensions:

1. The opposite parallel side (3 feet): \[ \text{Scale Length} = 3 \text{ feet} \times \frac{1}{4} = 0.75 \text{ feet} \]

2. The two legs (3 feet each): \[ \text{Scale Length} = 3 \text{ feet} \times \frac{1}{4} = 0.75 \text{ feet} \]

Thus, in the scale drawing, the lengths of the sides are as follows:

• Longest side: 1.5 feet
• Opposite parallel side: 0.75 feet
• Two legs: 0.75 feet each

Therefore, the final answer for the lengths of the other sides of the table is:

0.75 feet for both the parallel side and the legs.