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An illustration shows two parallelograms positioned in different ways. One shows the longer side along the base, and the other is tilted upward to the left, with a longer vertical side. The first parallelogram shows one parallel side as 5 inches and the adjacent side as 3.5 inches. The second parallelogram shows one parallel side as 0.7 inches and the adjacent vertical side as 1 inch.

Kamla draws the parallelogram on the left and then uses a scale factor to create the parallelogram on the right. All measurements are in inches. What scale factor does he use?

(1 point)
Responses

5
5

3.5
3.5

4
4

0.2
0.2
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1 answer

To determine the scale factor used by Kamla, we need to compare the corresponding sides of the two parallelograms.

In the first parallelogram:

  • One side is 5 inches.
  • The adjacent side is 3.5 inches.

In the second parallelogram:

  • One side is 0.7 inches (corresponding to the 5 inches side of the first parallelogram).
  • The adjacent side is 1 inch (corresponding to the 3.5 inches side of the first parallelogram).

Now, we calculate the scale factor for each corresponding pair of sides:

  1. For the longer sides: \[ \text{Scale Factor} = \frac{\text{Length of side in 2nd parallelogram}}{\text{Length of side in 1st parallelogram}} = \frac{0.7}{5} = 0.14 \]

  2. For the shorter sides: \[ \text{Scale Factor} = \frac{\text{Length of side in 2nd parallelogram}}{\text{Length of side in 1st parallelogram}} = \frac{1}{3.5} \approx 0.2857 \]

Since the scale factors for both pairs of corresponding sides need to be the same for them to be similar shapes, and they are not, we can conclude that there might have been a mistake in the observed dimensions or descriptions. However, based on the values provided for the second parallelogram, it appears we are being asked for a specific scale factor given in the responses.

To determine the correct answer from the options provided:

  • The closest value that fits within a reasonable small scale factor is \(0.2\).

Thus, Kamla likely used a scale factor of 0.2.