What is the length of the median from vertex A to side BC in triangle ABC, where

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Question: What is the length of the median from vertex A to side BC in triangle ABC, where AB = 10 cm, AC = 6 cm, and BC = 8 cm? (2023)

Options:

Correct Answer: 7 cm

Exam Year: 2023

Solution:

Using the median formula: m_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2), where a = BC, b = AC, c = AB. m_a = 1/2 * sqrt(2*6^2 + 2*10^2 - 8^2) = 7 cm.

What is the length of the median from vertex A to side BC in triangle ABC, where AB = 10 cm, AC = 6 cm, and BC = 8 cm? (2023)

What is the length of the median from vertex A to side BC in triangle ABC, where AB = 10 cm, AC = 6 cm, and BC = 8 cm? (2023)

Step 1: Identify the sides of triangle ABC. We have AB = 10 cm, AC = 6 cm, and BC = 8 cm.
Step 2: Assign the sides to the variables in the median formula. Let a = BC = 8 cm, b = AC = 6 cm, and c = AB = 10 cm.
Step 3: Write down the median formula: m_a = 1/2 * sqrt(2b^2 + 2c^2 - a^2).
Step 4: Substitute the values into the formula: m_a = 1/2 * sqrt(2*6^2 + 2*10^2 - 8^2).
Step 5: Calculate 6^2, which is 36, and 10^2, which is 100. So, 2*6^2 = 2*36 = 72 and 2*10^2 = 2*100 = 200.
Step 6: Now calculate a^2, which is 8^2 = 64.
Step 7: Substitute these values back into the formula: m_a = 1/2 * sqrt(72 + 200 - 64).
Step 8: Simplify inside the square root: 72 + 200 - 64 = 208.
Step 9: Now calculate the square root: sqrt(208).
Step 10: Find the approximate value of sqrt(208), which is about 14.42.
Step 11: Finally, multiply by 1/2: m_a = 1/2 * 14.42 = 7.21 cm.
Step 12: Round the answer to the nearest whole number if needed, which gives us approximately 7 cm.

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