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If triangle DEF is similar to triangle XYZ, and the sides of DEF are 4 cm, 6 cm,

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Question: If triangle DEF is similar to triangle XYZ, and the sides of DEF are 4 cm, 6 cm, and 8 cm, what is the ratio of the sides of triangle XYZ if the shortest side is 2 cm?

Options:

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

Correct Answer: 2:3

Solution: 

The ratio of the sides of similar triangles is constant. If the shortest side of DEF is 4 cm and XYZ is 2 cm, the ratio is 2:3.

If triangle DEF is similar to triangle XYZ, and the sides of DEF are 4 cm, 6 cm,

Practice Questions

Q1
If triangle DEF is similar to triangle XYZ, and the sides of DEF are 4 cm, 6 cm, and 8 cm, what is the ratio of the sides of triangle XYZ if the shortest side is 2 cm?
  1. 1:2
  2. 2:3
  3. 1:3
  4. 2:4

Questions & Step-by-Step Solutions

If triangle DEF is similar to triangle XYZ, and the sides of DEF are 4 cm, 6 cm, and 8 cm, what is the ratio of the sides of triangle XYZ if the shortest side is 2 cm?
  • Step 1: Identify the sides of triangle DEF. They are 4 cm, 6 cm, and 8 cm.
  • Step 2: Determine the shortest side of triangle DEF, which is 4 cm.
  • Step 3: Identify the shortest side of triangle XYZ, which is given as 2 cm.
  • Step 4: Set up the ratio of the shortest sides of the triangles. This is 2 cm (XYZ) to 4 cm (DEF).
  • Step 5: Simplify the ratio 2:4 by dividing both numbers by 2. This gives you 1:2.
  • Step 6: Since the triangles are similar, the ratio of all corresponding sides will be the same. Therefore, the ratio of the sides of triangle XYZ to triangle DEF is 1:2.
  • Step 7: To find the ratios of the other sides of triangle XYZ, multiply the sides of DEF (6 cm and 8 cm) by 1/2. This gives you 3 cm (for 6 cm) and 4 cm (for 8 cm).
  • Similarity of Triangles – Understanding that similar triangles have proportional sides.
  • Ratio Calculation – Calculating the ratio of corresponding sides based on the lengths given.
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