Question

Prove that 6 is the mean proportional between 4 and 9.

Answer 1

let A be the mean proportional between 4 and 9,

then
A/4 = 9/A,

A×A=9×4,

A²=36,

A=√36,

A=6,

hence proved

Answer 2

GM(4,9) = √(4×9) = √(36) = 6  

So 6 is the mean proportional (geometric mean) of four and nine.

The reason it is called the mean proportional is that the question can

also be written as a proportion. We want to find a number x for 4 and

9 so that the following proportion is true:

   4     x

  --- = ---

   x     9

If we set the cross products equal and get x² = 36, you can see why we

use the method above to get the same answer.