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If triangle JKL is similar to triangle MNO, and the lengths of JK and MN are 5 c

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

Options:

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

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 JKL is similar to triangle MNO, and the lengths of JK and MN are 5 c

Practice Questions

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

Questions & Step-by-Step Solutions

If triangle JKL is similar to triangle MNO, and the lengths of JK and MN are 5 cm and 10 cm respectively, what is the ratio of their areas?
  • Step 1: Understand that triangle JKL is similar to triangle MNO. This means they have the same shape but may be different sizes.
  • Step 2: Identify the lengths of the corresponding sides. Here, JK is 5 cm and MN is 10 cm.
  • Step 3: Find the ratio of the lengths of the corresponding sides. This is done by dividing the length of JK by the length of MN: 5 cm / 10 cm = 1/2.
  • Step 4: To find the ratio of the areas of the triangles, square the ratio of the sides. So, (1/2)² = 1/4.
  • Step 5: Conclude that the ratio of the areas of triangle JKL to triangle MNO 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 by squaring the ratio of the lengths of corresponding sides.
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