Geometry and TrigonometryHardSide ratio from an area ratio
Geometry and Trigonometry practice question
Two similar triangles have areas of 18 and 50 square units. What is the ratio of a side of the smaller triangle to the corresponding side of the larger triangle?
Answer: 3/5 or 0.6
Areas of similar figures scale with the SQUARE of the side ratio. 18/50 = 9/25 = (3/5)², so the side ratio is 3/5.
Common wrong answers
- If you answered 9/25
- 9/25 is the AREA ratio; the side ratio is its square root.
- If you answered 18/50
- 18/50 is the unsimplified area ratio, again not the side ratio.
- If you answered 5/3
- 5/3 is the ratio the other way round (larger to smaller).
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