Use your knowledge of similar figures and ratios to answer the following questions. This activity will give you a chance to practice the skills that were discussed in the video. When you have answered all of the questions, be sure to compare your answers against those that are given at the end.
Amusement Park Train
These rectangles are part of a set of plans for manufacturing a miniature train. The larger shape represents the side of a real-life boxcar, while the smaller shape represents the side of a boxcar that will be pulled by a miniature locomotive engine. The little train will be built to scale and shipped to an amusement park.
What scale is being used to build the miniature train? Write the scale or common ratio in at least two ways. (Hint: To find the common ratio, first write the ratios of the corresponding sides.)
Model Car
These quadrilaterals represent car doors in a kit for building a die cast model car. One quadrilateral represents a smaller-scale model car than the other.
What is the relationship between the two model cars in terms of scale? (Hint: Find the common ratio. Be sure to write it in at least two ways.)
| Your Responses | Sample Answers |
|---|---|
| The ratio of the widths is 2:8 or \(\mathsf{ \frac{2}{8} }\). The ratio of the lengths is 6:24 or \(\mathsf{ \frac{6}{24} }\). That makes the common ratio 1:4 or \(\mathsf{ \frac{1}{4} }\). The miniature train will be manufactured on a 1:4 scale. |
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| The ratios are as follows: 5:10 or \(\mathsf{ \frac{5}{10} }\) 2:4 or \(\mathsf{ \frac{2}{4} }\) 3:6 or \(\mathsf{ \frac{3}{6} }\) 1:2 or \(\mathsf{ \frac{1}{2} }\) The common ratio is \(\mathsf{ \frac{1}{2} }\) since all the ratios reduce to \(\mathsf{ \frac{1}{2} }\). |
