Geometric Mean Worksheet
This worksheet focuses on understanding and applying the geometric mean in various mathematical contexts for Grade 11 students.
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Geometric Mean Worksheet
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Date:
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Read each question carefully and answer to the best of your ability. Show all your work for full credit.
1. What is the geometric mean of 4 and 9?
5
6
6.5
13
2. In a right triangle, the altitude to the hypotenuse divides the hypotenuse into two segments. If the segments are of length 'a' and 'b', the altitude is the geometric mean of:
a and b
a and (a+b)
b and (a+b)
a, b, and (a+b)
3. The geometric mean of two positive numbers 'x' and 'y' is given by the formula GM = .
4. If the geometric mean of two numbers is 10 and one of the numbers is 5, the other number is .
5. Find the geometric mean of 2, 8, and 32.
6. In a right triangle, the altitude to the hypotenuse divides the hypotenuse into segments of length 3 cm and 12 cm. Find the length of the altitude.
7. The arithmetic mean of two distinct positive numbers is always greater than their geometric mean.
True
False
8. A rectangle has sides with lengths in the ratio 2:3. If the geometric mean of its side lengths is 6, find the actual lengths of the sides.
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