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If triangle DEF is similar to triangle XYZ and the sides of DEF are 3 cm, 4 cm,

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Question: If triangle DEF is similar to triangle XYZ and the sides of DEF are 3 cm, 4 cm, and 5 cm, what are the lengths of the corresponding sides of triangle XYZ if the ratio of similarity is 2:1?

Options:

  1. 6 cm, 8 cm, 10 cm
  2. 3 cm, 4 cm, 5 cm
  3. 1.5 cm, 2 cm, 2.5 cm
  4. 4 cm, 5 cm, 6 cm

Correct Answer: 6 cm, 8 cm, 10 cm

Solution: 

If the ratio of similarity is 2:1, then the sides of triangle XYZ will be 2 times the sides of triangle DEF, giving 6 cm, 8 cm, and 10 cm.

If triangle DEF is similar to triangle XYZ and the sides of DEF are 3 cm, 4 cm,

Practice Questions

Q1
If triangle DEF is similar to triangle XYZ and the sides of DEF are 3 cm, 4 cm, and 5 cm, what are the lengths of the corresponding sides of triangle XYZ if the ratio of similarity is 2:1?
  1. 6 cm, 8 cm, 10 cm
  2. 3 cm, 4 cm, 5 cm
  3. 1.5 cm, 2 cm, 2.5 cm
  4. 4 cm, 5 cm, 6 cm

Questions & Step-by-Step Solutions

If triangle DEF is similar to triangle XYZ and the sides of DEF are 3 cm, 4 cm, and 5 cm, what are the lengths of the corresponding sides of triangle XYZ if the ratio of similarity is 2:1?
  • Step 1: Understand that triangle DEF is similar to triangle XYZ, which means their sides are in proportion.
  • Step 2: Note the lengths of the sides of triangle DEF, which are 3 cm, 4 cm, and 5 cm.
  • Step 3: Identify the ratio of similarity, which is given as 2:1. This means that for every 1 unit of length in triangle DEF, triangle XYZ has 2 units.
  • Step 4: To find the lengths of the corresponding sides of triangle XYZ, multiply each side of triangle DEF by 2.
  • Step 5: Calculate the first side: 3 cm (DEF) * 2 = 6 cm (XYZ).
  • Step 6: Calculate the second side: 4 cm (DEF) * 2 = 8 cm (XYZ).
  • Step 7: Calculate the third side: 5 cm (DEF) * 2 = 10 cm (XYZ).
  • Step 8: Conclude that the lengths of the corresponding sides of triangle XYZ are 6 cm, 8 cm, and 10 cm.
  • Similarity of Triangles – Understanding that similar triangles have proportional sides based on a given ratio.
  • Ratio and Proportion – Applying the concept of ratios to find corresponding side lengths in similar figures.
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