Question

Find the mean proportional between 144 and 225

Answer 1

Let the mean between 144 and 225 is x
144:x = x:225
⇒ x² = 32400
⇒ x = 180
180 is the mean proportion between 144 and 225

Answer 2

let the mean proportional between 144 and 255 be x
144:x::x:255
x^2= 144×255
X = root of 144×255
X = root of 32300
X = 180