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If triangle DEF is similar to triangle XYZ and the length of DE is 6 and XY is 9

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Question: If triangle DEF is similar to triangle XYZ and the length of DE is 6 and XY is 9, what is the ratio of their areas?

Options:

  1. 2:3
  2. 3:4
  3. 4:5
  4. 1:1

Correct Answer: 2:3

Solution: 

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (6/9)² = (2/3)² = 4/9.

If triangle DEF is similar to triangle XYZ and the length of DE is 6 and XY is 9

Practice Questions

Q1
If triangle DEF is similar to triangle XYZ and the length of DE is 6 and XY is 9, what is the ratio of their areas?
  1. 2:3
  2. 3:4
  3. 4:5
  4. 1:1

Questions & Step-by-Step Solutions

If triangle DEF is similar to triangle XYZ and the length of DE is 6 and XY is 9, what is the ratio of their areas?
  • Step 1: Identify the lengths of the corresponding sides of the triangles. Here, DE = 6 and XY = 9.
  • Step 2: Find the ratio of the lengths of the corresponding sides. This is done by dividing DE by XY: 6 / 9.
  • Step 3: Simplify the ratio 6 / 9. This simplifies to 2 / 3.
  • Step 4: To find the ratio of the areas of the triangles, square the ratio of the sides. So, (2 / 3)² = 4 / 9.
  • Step 5: The ratio of the areas of triangle DEF to triangle XYZ 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 Triangles – The ratio of the areas of similar triangles is equal to the square of the ratio of their corresponding side lengths.
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