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Geometric Mean Worksheet

This worksheet focuses on understanding and applying the geometric mean in various mathematical contexts for Grade 11 students.

Grade 11 Math GeometryGeometric Mean
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Includes

Multiple ChoiceFill in the BlanksShort AnswerTrue / FalseLong Answer

Standards

CCSS.MATH.CONTENT.HSG.SRT.B.5CCSS.MATH.CONTENT.HSG.GPE.B.7

Topics

geometric meangeometrymathgrade 11
7 sections · Free to use · Printable
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Geometric Mean Worksheet

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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?

a

5

b

6

c

6.5

d

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

a and b

b

a and (a+b)

c

b and (a+b)

d

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.

3 cm12 cmh

7. The arithmetic mean of two distinct positive numbers is always greater than their geometric mean.

T

True

F

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.