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What is the length of the altitude from vertex A to side BC in triangle ABC with

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Question: What is the length of the altitude from vertex A to side BC in triangle ABC with sides 5 cm, 12 cm, and 13 cm?

Options:

  1. 5 cm
  2. 6 cm
  3. 12 cm
  4. 13 cm

Correct Answer: 6 cm

Solution: 

The area of the triangle can be calculated as (1/2) * base * height. The area is 30 cm² (since it\'s a right triangle). Using area = (1/2) * 12 * height, we find height = 5 cm.

What is the length of the altitude from vertex A to side BC in triangle ABC with

Practice Questions

Q1
What is the length of the altitude from vertex A to side BC in triangle ABC with sides 5 cm, 12 cm, and 13 cm?
  1. 5 cm
  2. 6 cm
  3. 12 cm
  4. 13 cm

Questions & Step-by-Step Solutions

What is the length of the altitude from vertex A to side BC in triangle ABC with sides 5 cm, 12 cm, and 13 cm?
  • Step 1: Identify the sides of triangle ABC. The sides are 5 cm, 12 cm, and 13 cm.
  • Step 2: Determine if the triangle is a right triangle. Since 5² + 12² = 13² (25 + 144 = 169), it is a right triangle.
  • Step 3: In a right triangle, the area can be calculated using the formula: Area = (1/2) * base * height. Here, we can use the two shorter sides (5 cm and 12 cm) as the base and height.
  • Step 4: Calculate the area of the triangle: Area = (1/2) * 5 * 12 = 30 cm².
  • Step 5: Now, we need to find the altitude (height) from vertex A to side BC. We can use the area formula again: Area = (1/2) * base * height, where the base is side BC (which is 12 cm).
  • Step 6: Set up the equation using the area we found: 30 cm² = (1/2) * 12 * height.
  • Step 7: Solve for height: 30 = 6 * height, so height = 30 / 6 = 5 cm.
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