Middle School Math Quiz: Dilations And Similarity
3 questions · exam conditions
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Dilations And SimilarityQuestion 1 of 3

Triangle ABC is dilated by a scale factor of 34\frac{3}{4} to create triangle A'B'C'. If the perimeter of triangle ABC is 28 units and the area is 42 square units, what is the area of triangle A'B'C'?

31.5 square units
23.625 square units
21 square units
56 square units
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Middle School Math Quiz

Middle School Math Quiz: Dilations And Similarity

Practice Dilations And Similarity in Middle School Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Dilations And Similarity, giving you a quick way to practice the rules, question types, and explanations that matter most for Middle School Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

Triangle ABC is dilated by a scale factor of 34\frac{3}{4} to create triangle A'B'C'. If the perimeter of triangle ABC is 28 units and the area is 42 square units, what is the area of triangle A'B'C'?

  1. 31.5 square units
  2. 23.625 square units (correct answer)
  3. 21 square units
  4. 56 square units
Explanation: When a figure is dilated by scale factor k, the area is multiplied by k². Here, k = 3/4, so k² = 9/16. The new area is 42 × 9/16 = 23.625 square units. Choice A incorrectly multiplies perimeter by scale factor. Choice C incorrectly divides original area by 2. Choice D incorrectly multiplies area by scale factor instead of scale factor squared.

Question 2

Two similar triangles have areas in the ratio 16:25. If a dilation with scale factor k transforms the smaller triangle so that it becomes congruent to the larger triangle, what is the value of k?

  1. 45\frac{4}{5}
  2. 54\frac{5}{4} (correct answer)
  3. 916\frac{9}{16}
  4. 2516\frac{25}{16}
Explanation: If area ratio is 16:25, then the ratio of corresponding sides is √16:√25 = 4:5. To make the smaller triangle congruent to the larger, we need scale factor k = 5/4. Choice A gives the ratio of smaller to larger sides. Choice C incorrectly uses (5-4)/16. Choice D uses the area ratio instead of side ratio.

Question 3

Circle A has radius 8 units and circle B has radius 12 units. If circle A is dilated by scale factor m and circle B is dilated by scale factor n, and both resulting circles are congruent, which equation correctly relates m and n?

  1. 8m = 12n (correct answer)
  2. 8m + 12n = 20
  3. 64m² = 144n²
  4. m/n = 8/12
Explanation: For the dilated circles to be congruent, they must have equal radii: 8m = 12n. This means the final radius of circle A after dilation equals the final radius of circle B after dilation. Choice B incorrectly adds the expressions. Choice C relates areas instead of radii. Choice D gives the wrong ratio relationship.