Geometry and TrigonometryHardSide of a similar triangle from an area ratio
Geometry and Trigonometry practice question
Triangle ABC is similar to triangle DEF, and the area of triangle ABC is 9 times the area of triangle DEF. If AB = 12, what is the length of the corresponding side DE?
Answer: 4
Areas scale by the square of the length ratio, so lengths are in the ratio 3 : 1 and DE = 12/3 = 4.
Common wrong answers
- If you answered 36
- 36 multiplies 12 by 3.
- If you answered 108
- 108 multiplies 12 by 9.
- If you answered 1.33
- 1.33 divides 12 by 9, using the area ratio as a length ratio.
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