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If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY i

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Question: If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY is 8 cm, what is the ratio of the lengths of corresponding sides?

Options:

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

Correct Answer: 1:2

Solution: 

The ratio of the lengths of corresponding sides of similar triangles is equal to the ratio of any two corresponding sides, which is 4:8 or 1:2.

If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY i

Practice Questions

Q1
If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY is 8 cm, what is the ratio of the lengths of corresponding sides?
  1. 1:2
  2. 2:1
  3. 1:4
  4. 4:1

Questions & Step-by-Step Solutions

If triangle DEF is similar to triangle XYZ and the length of DE is 4 cm and XY is 8 cm, what is the ratio of the lengths of corresponding sides?
  • Step 1: Understand that triangle DEF is similar to triangle XYZ. This means their corresponding sides are in the same ratio.
  • Step 2: Identify the lengths of the corresponding sides given in the question. DE is 4 cm and XY is 8 cm.
  • Step 3: Write the ratio of the lengths of DE to XY. This is 4 cm (DE) to 8 cm (XY).
  • Step 4: Simplify the ratio 4:8. Divide both numbers by 4.
  • Step 5: The simplified ratio is 1:2.
  • Similarity of Triangles – Triangles are similar if their corresponding angles are equal and their corresponding sides are in proportion.
  • Ratio of Corresponding Sides – The ratio of the lengths of corresponding sides of similar triangles is constant and can be derived from any pair of corresponding sides.
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