If the medians of a triangle are 6, 8, and 10, what is the area of the triangle?
Practice Questions
1 question
Q1
If the medians of a triangle are 6, 8, and 10, what is the area of the triangle?
24
36
48
60
Area = (4/3) * √(s(s - m1)(s - m2)(s - m3)), where s = (6 + 8 + 10)/2 = 12. Area = (4/3) * √(12 * 6 * 4 * 2) = 48.
Questions & Step-by-step Solutions
1 item
Q
Q: If the medians of a triangle are 6, 8, and 10, what is the area of the triangle?
Solution: Area = (4/3) * √(s(s - m1)(s - m2)(s - m3)), where s = (6 + 8 + 10)/2 = 12. Area = (4/3) * √(12 * 6 * 4 * 2) = 48.
Steps: 10
Step 1: Identify the lengths of the medians of the triangle. They are given as 6, 8, and 10.
Step 2: Calculate the semi-perimeter 's' of the triangle formed by the medians. Use the formula s = (m1 + m2 + m3) / 2, where m1, m2, and m3 are the lengths of the medians.
Step 3: Substitute the values into the formula: s = (6 + 8 + 10) / 2 = 12.
Step 4: Use the area formula for a triangle based on its medians: Area = (4/3) * √(s * (s - m1) * (s - m2) * (s - m3)).
Step 5: Substitute the values into the area formula: Area = (4/3) * √(12 * (12 - 6) * (12 - 8) * (12 - 10)).
Step 6: Calculate the values inside the square root: Area = (4/3) * √(12 * 6 * 4 * 2).
