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In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?

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Question: In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?

Options:

  1. 12
  2. 14
  3. 16
  4. 18

Correct Answer: 14

Solution: 

Semi-perimeter s = (AB + AC + BC) / 2 = (8 + 6 + 10) / 2 = 12.

In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?

Practice Questions

Q1
In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?
  1. 12
  2. 14
  3. 16
  4. 18

Questions & Step-by-Step Solutions

In triangle ABC, if AB = 8, AC = 6, and BC = 10, what is the semi-perimeter?
  • Step 1: Identify the lengths of the sides of triangle ABC. We have AB = 8, AC = 6, and BC = 10.
  • Step 2: Add the lengths of all three sides together. Calculate 8 + 6 + 10.
  • Step 3: The sum of the sides is 24.
  • Step 4: To find the semi-perimeter, divide the total sum by 2. Calculate 24 / 2.
  • Step 5: The result is 12, which is the semi-perimeter of triangle ABC.
  • Triangle Properties – Understanding the properties of triangles, including the calculation of the semi-perimeter.
  • Perimeter Calculation – Ability to calculate the perimeter of a triangle and derive the semi-perimeter from it.
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