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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

4
4

3.5
3.5

5
5

0.2

1 answer

To find the scale factor from the first parallelogram to the second parallelogram, we can compare the corresponding sides of each figure.

For the first parallelogram:

  • One side is 5 inches (base).
  • The adjacent side is 3.5 inches (height).

For the second parallelogram:

  • One side is 0.7 inches (base).
  • The adjacent side is 1 inch (height).

Now, let's compare the lengths:

  1. The scale factor for the base from the first to the second parallelogram is: \[ \text{Scale factor (base)} = \frac{0.7}{5} = 0.14 \]

  2. The scale factor for the height from the first to the second parallelogram is: \[ \text{Scale factor (height)} = \frac{1}{3.5} = 0.2857 \text{ (approximately) } \]

Since we need a common scale factor that applies to both dimensions, it looks like neither value matches the given options of 4, 3.5, 5, or 0.2.

However, if we reverse our comparison and consider how to scale the smaller to match the larger dimensions:

  • To scale the height from 1 inch back to the first parallelogram's height of 3.5 inches: \[ \text{Scale factor} = \frac{3.5}{1} = 3.5 \]

  • To scale the base from 0.7 inches back up to 5 inches: \[ \text{Scale factor} = \frac{5}{0.7} \approx 7.14 \]

Here, the height's scaling factor is consistent with one of the choices given.

Thus, the scale factor Kamla uses is 3.5.