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If two triangles are similar and the ratio of their corresponding sides is 2:3,

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Question: If two triangles are similar and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?

Options:

  1. 4:9
  2. 2:3
  3. 3:4
  4. 1:2

Correct Answer: 4:9

Solution: 

Area ratio = (2/3)² = 4/9.

If two triangles are similar and the ratio of their corresponding sides is 2:3,

Practice Questions

Q1
If two triangles are similar and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?
  1. 4:9
  2. 2:3
  3. 3:4
  4. 1:2

Questions & Step-by-Step Solutions

If two triangles are similar and the ratio of their corresponding sides is 2:3, what is the ratio of their areas?
  • Step 1: Understand that similar triangles have corresponding sides that are in proportion.
  • Step 2: Note the given ratio of the corresponding sides, which is 2:3.
  • Step 3: To find the ratio of the areas of the triangles, square the ratio of the sides.
  • Step 4: Calculate (2/3)², which means 2² divided by 3².
  • Step 5: Calculate 2² = 4 and 3² = 9.
  • Step 6: Therefore, the area ratio is 4/9.
  • Similarity of Triangles – Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
  • Area Ratio of Similar Figures – The ratio of the areas of two similar figures is equal to the square of the ratio of their corresponding side lengths.
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