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If triangle GHI is similar to triangle JKL and the sides of triangle GHI are 3 c

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Question: If triangle GHI is similar to triangle JKL and the sides of triangle GHI are 3 cm, 4 cm, and 5 cm, what is the ratio of the sides of triangle JKL if the longest side is 10 cm?

Options:

  1. 2:1
  2. 3:2
  3. 5:2
  4. 4:1

Correct Answer: 2:1

Solution: 

The ratio of the longest sides is 10 cm to 5 cm, which simplifies to 2:1. Therefore, the sides of triangle JKL are in the ratio 2:1.

If triangle GHI is similar to triangle JKL and the sides of triangle GHI are 3 c

Practice Questions

Q1
If triangle GHI is similar to triangle JKL and the sides of triangle GHI are 3 cm, 4 cm, and 5 cm, what is the ratio of the sides of triangle JKL if the longest side is 10 cm?
  1. 2:1
  2. 3:2
  3. 5:2
  4. 4:1

Questions & Step-by-Step Solutions

If triangle GHI is similar to triangle JKL and the sides of triangle GHI are 3 cm, 4 cm, and 5 cm, what is the ratio of the sides of triangle JKL if the longest side is 10 cm?
  • Step 1: Identify the sides of triangle GHI. They are 3 cm, 4 cm, and 5 cm.
  • Step 2: Determine which side is the longest in triangle GHI. The longest side is 5 cm.
  • Step 3: Identify the longest side of triangle JKL, which is given as 10 cm.
  • Step 4: Set up the ratio of the longest sides of triangle JKL to triangle GHI. This is 10 cm (JKL) to 5 cm (GHI).
  • Step 5: Simplify the ratio 10 cm to 5 cm. Divide both numbers by 5.
  • Step 6: The simplified ratio is 2:1.
  • Step 7: Since the triangles are similar, the sides of triangle JKL are in the same ratio as triangle GHI, which is 2:1.
  • Similarity of Triangles – Understanding that similar triangles have proportional sides.
  • Ratio and Proportion – Calculating the ratio of corresponding sides based on the longest side.
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