Geometry and TrigonometryHardSimilar triangles from their perimeters
Geometry and Trigonometry practice question
Two triangles are similar. The perimeter of the smaller is 18 and the perimeter of the larger is 27. A side of the smaller triangle has length 4. What is the length of the corresponding side of the larger triangle?
Answer: 6
Perimeters of similar figures are in the same ratio as corresponding sides: 27/18 = 3/2. So the corresponding side is 4 × 3/2 = 6.
Common wrong answers
- If you answered 9
- 9 is 4 × 9/4, using the perimeter difference (9) over the side. The scale factor is 27/18.
- If you answered 13
- 13 is 4 + 9, adding the difference in perimeters. Similar figures scale by a ratio, not a fixed amount.
- If you answered 2.67
- 2.67 scales the wrong way (4 × 18/27); the larger triangle has the larger side.
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