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

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Question: What is the length of the median from vertex A to side BC in triangle ABC with sides AB = 6 cm, AC = 8 cm, and BC = 10 cm?

Options:

Correct Answer: 7 cm

Solution:

The length of the median can be calculated using the formula: median = 1/2 * √(2AB^2 + 2AC^2 - BC^2) = 1/2 * √(2*6^2 + 2*8^2 - 10^2) = 7 cm.

What is the length of the median from vertex A to side BC in triangle ABC with sides AB = 6 cm, AC = 8 cm, and BC = 10 cm?

What is the length of the median from vertex A to side BC in triangle ABC with sides AB = 6 cm, AC = 8 cm, and BC = 10 cm?

Step 1: Identify the sides of triangle ABC. We have AB = 6 cm, AC = 8 cm, and BC = 10 cm.
Step 2: Write down the formula for the length of the median from vertex A to side BC: median = 1/2 * √(2AB^2 + 2AC^2 - BC^2).
Step 3: Substitute the values of AB, AC, and BC into the formula: median = 1/2 * √(2*6^2 + 2*8^2 - 10^2).
Step 4: Calculate AB^2, AC^2, and BC^2: 6^2 = 36, 8^2 = 64, and 10^2 = 100.
Step 5: Multiply the squares by 2: 2*6^2 = 72 and 2*8^2 = 128.
Step 6: Add the results: 72 + 128 = 200.
Step 7: Subtract BC^2 from the sum: 200 - 100 = 100.
Step 8: Take the square root of the result: √100 = 10.
Step 9: Multiply by 1/2: 1/2 * 10 = 5.
Step 10: The length of the median from vertex A to side BC is 5 cm.

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