Multiple choice

Similar triangles ABC and DEF have their areas in the ratio 16 : 25. Which of the following cannot be their corresponding sides?

  1. 4 cm and 5 cm

  2. 8 cm and 10 cm

  3. 12 cm and 15 cm

  4. 16 cm and 25 cm
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The ratio of areas of similar triangles is the square of the ratio of their corresponding sides. Since 16:25 = (4:5)^2, the sides must be in the ratio 4:5. Option D (16:25) is not in the ratio 4:5.

AI explanation

By the property of similar triangles, the ratio of corresponding sides equals the square root of the ratio of their areas. Taking the square root of the 16:25 area ratio gives a corresponding side ratio of 4:5. Evaluating the options, 4 and 5, 8 and 10, and 12 and 15 all simplify to this ratio, whereas 16 and 25 simplifies to 16:25, so this cannot be the correct pair of sides.

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