Question

find the mean proportional between 2 and 32.

Answer 1

Answer:

8

Step-by-step explanation:

Let the mean proportional be x

A/q 2:x : : x:32

=>2/x × x/32

=> 2×32 = x×x

=> 64 = x²

=> x² = 64

=> x = √64

=> x = 8 (Ans)

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Answer 2

The mean proportional between 2 and 32 is 8.

Given:

Two numbers, 2 and 32.

To Find:

The mean proportional between 2 and 32.

Solution:

Mean proportion is also known as the geometric mean.

Let p and q be two positive numbers. Then the mean proportion, say x, is:

a : x :: x : b or a/x = x/b or $\sqrt{ab}$ = x

i.e. mean proportion of two numbers is the square root of the product of those numbers.

The given numbers are 2 and 5. Let us assume that the mean proportion of these two numbers is x.

⇒ 2: x :: x :5

⇒ 2/x = x/5

⇒ x² = 10

⇒ x = 5.

Hence, the mean proportional between 2 and 32 is 8.

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