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If triangle GHI is similar to triangle JKL, and the lengths of sides GH and JK a

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Question: If triangle GHI is similar to triangle JKL, and the lengths of sides GH and JK are 5 cm and 10 cm respectively, what is the ratio of their areas?

Options:

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

Correct Answer: 1:4

Solution: 

The ratio of the areas of similar triangles is the square of the ratio of their corresponding sides. (5/10)^2 = 1/4.

If triangle GHI is similar to triangle JKL, and the lengths of sides GH and JK a

Practice Questions

Q1
If triangle GHI is similar to triangle JKL, and the lengths of sides GH and JK are 5 cm and 10 cm respectively, what is the ratio of their areas?
  1. 1:2
  2. 1:4
  3. 2:1
  4. 4:1

Questions & Step-by-Step Solutions

If triangle GHI is similar to triangle JKL, and the lengths of sides GH and JK are 5 cm and 10 cm respectively, what is the ratio of their areas?
  • Step 1: Understand that triangle GHI is similar to triangle JKL. This means their shapes are the same, but their sizes may be different.
  • Step 2: Identify the lengths of the corresponding sides. Here, side GH of triangle GHI is 5 cm, and side JK of triangle JKL is 10 cm.
  • Step 3: Write the ratio of the lengths of the corresponding sides. The ratio of GH to JK is 5 cm to 10 cm, which can be written as 5/10.
  • Step 4: Simplify the ratio 5/10. This simplifies to 1/2.
  • Step 5: To find the ratio of the areas of the triangles, square the ratio of the sides. So, (1/2) squared is (1/2) * (1/2) = 1/4.
  • Step 6: Conclude that the ratio of the areas of triangle GHI to triangle JKL is 1/4.
  • Similarity of Triangles – Understanding that similar triangles have proportional sides and that the ratio of their areas is the square of the ratio of their corresponding sides.
  • Area Ratio Calculation – Calculating the area ratio using the formula that relates the ratio of sides to the ratio of areas.
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