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Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, an

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Question: Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the length of the corresponding side in the second triangle if its longest side is 10 cm?

Options:

  1. 6 cm
  2. 8 cm
  3. 10 cm
  4. 12 cm

Correct Answer: 8 cm

Solution: 

The ratio of the sides is 10/5 = 2. Therefore, the corresponding side is 4 * 2 = 8 cm.

Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, an

Practice Questions

Q1
Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the length of the corresponding side in the second triangle if its longest side is 10 cm?
  1. 6 cm
  2. 8 cm
  3. 10 cm
  4. 12 cm

Questions & Step-by-Step Solutions

Two triangles are similar. If the sides of the first triangle are 3 cm, 4 cm, and 5 cm, what is the length of the corresponding side in the second triangle if its longest side is 10 cm?
  • Step 1: Identify the sides of the first triangle. They are 3 cm, 4 cm, and 5 cm.
  • Step 2: Determine which side of the first triangle is the longest. The longest side is 5 cm.
  • Step 3: Identify the longest side of the second triangle, which is given as 10 cm.
  • Step 4: Calculate the ratio of the longest sides of the two triangles. The ratio is 10 cm (second triangle) divided by 5 cm (first triangle), which equals 2.
  • Step 5: Use the ratio to find the corresponding side in the second triangle. The corresponding side to 4 cm in the first triangle is calculated as 4 cm multiplied by the ratio of 2, which equals 8 cm.
  • Similarity of Triangles – Understanding that similar triangles have proportional sides.
  • Ratio and Proportion – Using the ratio of corresponding sides to find unknown lengths.
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