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If triangle GHI is similar to triangle JKL and the length of side GH is 5 cm whi

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Question: If triangle GHI is similar to triangle JKL and the length of side GH is 5 cm while side JK is 10 cm, what is the ratio of the areas of the two triangles?

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. (10/5)^2 = 2^2 = 4, so the ratio of the areas is 1:4.

If triangle GHI is similar to triangle JKL and the length of side GH is 5 cm whi

Practice Questions

Q1
If triangle GHI is similar to triangle JKL and the length of side GH is 5 cm while side JK is 10 cm, what is the ratio of the areas of the two triangles?
  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 length of side GH is 5 cm while side JK is 10 cm, what is the ratio of the areas of the two triangles?
  • Step 1: Identify the lengths of the corresponding sides of the triangles. Here, side GH of triangle GHI is 5 cm and side JK of triangle JKL is 10 cm.
  • Step 2: Write the ratio of the lengths of the corresponding sides. The ratio of side JK to side GH is 10 cm to 5 cm, which can be written as 10/5.
  • Step 3: Simplify the ratio 10/5. This simplifies to 2/1.
  • Step 4: To find the ratio of the areas of the triangles, square the ratio of the sides. So, (2/1)^2 = 2^2 = 4.
  • Step 5: The ratio of the areas of triangle GHI to triangle JKL is 1:4, meaning triangle GHI has 1 part area for every 4 parts area of triangle JKL.
  • 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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