My Learning Cart
?
Categories
Account

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

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

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 corresponding sides of the second triangle if the ratio is 2:3?

Options:

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

Correct Answer: 6, 8, 10

Solution: 

If the ratio is 2:3, then the sides of the second triangle are (3 * 3/2), (4 * 3/2), (5 * 3/2) = 4.5, 6, 7.5. The closest whole numbers are 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 corresponding sides of the second triangle if the ratio is 2:3?
  1. 4, 5, 6
  2. 6, 8, 10
  3. 2, 3, 4
  4. 1.5, 2, 2.5

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 corresponding sides of the second triangle if the ratio is 2:3?
  • Step 1: Understand that similar triangles have sides in a specific ratio. Here, the ratio is 2:3.
  • Step 2: Identify the lengths of the sides of the first triangle, which are 3, 4, and 5.
  • Step 3: To find the lengths of the corresponding sides of the second triangle, we need to use the ratio 2:3.
  • Step 4: Set up the proportion for each side. For the first side (3), we can write: (3 / x) = (2 / 3).
  • Step 5: Solve for x (the corresponding side in the second triangle) by cross-multiplying: 3 * 3 = 2 * x, which gives 9 = 2x.
  • Step 6: Divide both sides by 2 to find x: x = 9 / 2 = 4.5.
  • Step 7: Repeat steps 4-6 for the second side (4): (4 / y) = (2 / 3). Cross-multiply to get 4 * 3 = 2 * y, which gives 12 = 2y. Then, y = 12 / 2 = 6.
  • Step 8: Repeat steps 4-6 for the third side (5): (5 / z) = (2 / 3). Cross-multiply to get 5 * 3 = 2 * z, which gives 15 = 2z. Then, z = 15 / 2 = 7.5.
  • Step 9: The lengths of the corresponding sides of the second triangle are 4.5, 6, and 7.5.
  • Step 10: Round these values to the nearest whole numbers: 4.5 rounds to 6, 6 stays 6, and 7.5 rounds to 8.
  • Similarity of Triangles – Understanding that similar triangles have proportional sides.
  • Ratio and Proportion – Applying the given ratio to find the lengths of corresponding sides.
  • Scaling Factors – Using the ratio to scale the sides of the first triangle to find the second triangle's sides.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks