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If the ratio of the lengths of two sides of a triangle is 3:4 and the length of

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Question: If the ratio of the lengths of two sides of a triangle is 3:4 and the length of the shorter side is 9 cm, what is the length of the longer side? (2022)

Options:

  1. 12 cm
  2. 15 cm
  3. 18 cm
  4. 21 cm

Correct Answer: 12 cm

Exam Year: 2022

Solution: 

If the shorter side is 9 cm and the ratio is 3:4, then the longer side is (4/3) × 9 cm = 12 cm.

If the ratio of the lengths of two sides of a triangle is 3:4 and the length of

Practice Questions

Q1
If the ratio of the lengths of two sides of a triangle is 3:4 and the length of the shorter side is 9 cm, what is the length of the longer side? (2022)
  1. 12 cm
  2. 15 cm
  3. 18 cm
  4. 21 cm

Questions & Step-by-Step Solutions

If the ratio of the lengths of two sides of a triangle is 3:4 and the length of the shorter side is 9 cm, what is the length of the longer side? (2022)
  • Step 1: Understand the ratio of the sides. The ratio 3:4 means for every 3 parts of the shorter side, the longer side has 4 parts.
  • Step 2: Identify the length of the shorter side. The problem states that the shorter side is 9 cm.
  • Step 3: Set up the relationship using the ratio. If the shorter side is 3 parts, then we can say 3 parts = 9 cm.
  • Step 4: Find the value of one part. To find the length of one part, divide the length of the shorter side by 3: 9 cm ÷ 3 = 3 cm per part.
  • Step 5: Calculate the length of the longer side. The longer side is 4 parts, so multiply the length of one part by 4: 3 cm × 4 = 12 cm.
  • Step 6: State the final answer. The length of the longer side is 12 cm.
  • Ratio and Proportion – Understanding how to apply ratios to find unknown lengths in geometric figures.
  • Triangle Properties – Knowledge of the properties of triangles, specifically relating to side lengths.
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