Question

Find the mean proportional of the following:

0.25, 40000

Answer 1

Let x be the mean proportional between 0.25 and 40000

Then,

0.25 : x :: x : 40000

⇒ 0.25 : x = x : 40000

⇒ `0.25/x = x/40000`

⇒ x² = 0.25 × 40000

⇒ x² = 10,000

⇒ x = `sqrt(10,000)`

⇒ x = 100