If two similar triangles have a scale factor of 2, and a corresponding side in the smaller triangle is 5, what is the corresponding side in the larger triangle?

• A. 10
• B. 5
• C. 15
• D. 20

Answer: (A)

Similar shapes have proportional corresponding lengths. A scale factor of 2 means the larger triangle is twice as large in every linear dimension as the smaller one. So any corresponding side in the larger triangle is 2 times the matching side in the smaller triangle. If the smaller side is 5, the larger side is 2 × 5 = 10. The other values would correspond to different scale factors: 5 would mean no change in size, 15 would be a factor of 3, and 20 would be a factor of 4.