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?
Choices:
4
5
0.2
3.5
Let the dimensions of the original parallelogram be $x$ inches by $y$ inches. Since the original parallelogram has one side of length 5 inches and an adjacent side of length 3.5 inches, we have the proportion $\frac{x}{y} = \frac{5}{3.5}$. Solving this equation gives $x = \frac{10}{7}y$.
Now consider the second parallelogram. Since the original parallelogram has dimensions $x$ inches by $y$ inches, the second parallelogram has dimensions $\frac{0.7}{5}x$ inches by $\frac{1}{3.5}y$ inches. So, the scale factor used is $\frac{\frac{0.7}{5}x}{x} = \frac{0.7}{5} \cdot \frac{10}{7} = \frac{7}{5} \cdot \frac{10}{7} = \boxed{2}$.