Question

Mean proportional of 12 and 192

Answer 1

Answer:

4 and 36.

Step-by-step explanation:

Let x and y be the two numbers. Then,

√x*y = 12 ( given mean proportion)

So, x*y = 12*12 = 144 (1)

Also, the third proportional of the two numbers is given as 324.

Therefore, x / y = y / 324

So, y^2 = 324 x

y = √324 x = 18 √x

Substituting this value of y in (1) above, we get:

x*18√x = 144

Therefore, x*√x = 144 / 18 = 8

Squaring both sides, we get:

x^2*x = 8*8 = 64

So, x^3 = 64

x = 4

Therefore, from (1) above, y = 144 / 4 = 36.

So, the two numbers are 4 and 36. Answer

Check:

Mean proportion of 4 and 36 = √ 4*36 = √144 =12 ✓

Third proportional , say, z of 4 and 36 is given by:

4 / 36 = 36 /z.

So, the third proportional, z works out to:

z = 36*36 / 4 = 36*9 = 324 ✓

Answer 2

Answer:

Let the mean proportion between 12 and 192 is x.

Accordingly,

$x^{2} = \sqrt{12*192}$                        

$x^{2} =\sqrt{2304}$    

$x = 48$

Therefore, the mean proportion between 12 and 192 is 48.

Step-by-step explanation:

The mean proportion or geometric mean of two positive numbers p and q is the positive number x , such that p/x = x/q. When solving the variable, x =$\sqrt{p * q}$

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