Question

find mean proportional of 6 and 24

Answer 1

Suppose that x is the mean proportional.
 
Then, 6 : x :: x : 24

⇒ 6 × 24 = x × x                                         (Product of extremes = Product of means)
⇒ x2  = 144
⇒ x = 12

Hence, the mean proportional to 6 and 24 is 12.

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