Geometry and TrigonometryHardCorresponding side from a perimeter ratio
Geometry and Trigonometry practice question
Two similar triangles have perimeters of 7 centimetres and 21 centimetres. The shortest side of the smaller triangle is 2 centimetres. What is the length, in centimetres, of the shortest side of the larger triangle?
Answer: 6
Perimeters of similar figures are in the same ratio as corresponding sides: 21/7 = 3, so 2 × 3 = 6.
Common wrong answers
- If you answered 3
- 3 is the scale factor, not the side.
- If you answered 16
- 16 adds the perimeter difference (14) to 2; similarity scales, it doesn't add.
- If you answered 18
- 18 scales by 3² = 9, which is how AREAS scale, not sides.
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