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If two triangles are similar and the lengths of the sides of the first triangle

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Question: If two triangles are similar and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the sides of the second triangle if the ratio of similarity is 2:1?

Options:

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

Correct Answer: 6, 8, 10

Solution: 

If the ratio of similarity is 2:1, then the sides of the second triangle are 2 times the sides of the first triangle: 3*2, 4*2, 5*2 = 6, 8, 10.

If two triangles are similar and the lengths of the sides of the first triangle

Practice Questions

Q1
If two triangles are similar and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the sides of the second triangle if the ratio of similarity is 2:1?
  1. 6, 8, 10
  2. 3, 4, 5
  3. 1.5, 2, 2.5
  4. 4, 5, 6

Questions & Step-by-Step Solutions

If two triangles are similar and the lengths of the sides of the first triangle are 3, 4, and 5, what are the lengths of the sides of the second triangle if the ratio of similarity is 2:1?
  • Step 1: Identify the lengths of the sides of the first triangle, which are 3, 4, and 5.
  • Step 2: Understand that the ratio of similarity is 2:1. This means the sides of the second triangle are 2 times the lengths of the sides of the first triangle.
  • Step 3: Calculate the length of the first side of the second triangle by multiplying the first side of the first triangle (3) by 2: 3 * 2 = 6.
  • Step 4: Calculate the length of the second side of the second triangle by multiplying the second side of the first triangle (4) by 2: 4 * 2 = 8.
  • Step 5: Calculate the length of the third side of the second triangle by multiplying the third side of the first triangle (5) by 2: 5 * 2 = 10.
  • Step 6: The lengths of the sides of the second triangle are 6, 8, and 10.
  • Similarity of Triangles – Understanding that similar triangles have proportional sides based on a given ratio.
  • Ratio and Proportion – Applying the concept of ratios to scale the lengths of the sides of triangles.
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