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If two similar triangles have a ratio of 2:3, what is the ratio of their areas?

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Question: If two similar triangles have a ratio of 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: 

The ratio of areas of similar triangles is the square of the ratio of their corresponding sides. Therefore, (2:3)² = 4:9.

If two similar triangles have a ratio of 2:3, what is the ratio of their areas?

Practice Questions

Q1
If two similar triangles have a ratio of 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 similar triangles have a ratio of 2:3, what is the ratio of their areas?
  • Step 1: Understand that similar triangles have the same shape but different sizes.
  • Step 2: Know that the ratio of the lengths of corresponding sides of the triangles is given as 2:3.
  • Step 3: To find the ratio of the areas, we need to square the ratio of the sides.
  • Step 4: Calculate (2:3) squared, which means you square both numbers: 2² and 3².
  • Step 5: 2² equals 4 and 3² equals 9.
  • Step 6: Therefore, the ratio of the areas of the two triangles is 4:9.
  • Similar Triangles – Triangles that have the same shape but may differ in size, with corresponding angles equal and corresponding sides in proportion.
  • Ratio of Areas – The ratio of the areas of similar figures is equal to the square of the ratio of their corresponding linear dimensions (sides).
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