Question

what is the mean proportion of 5,20

Answer 1

Let x be the mean proportion.

x/5 = x/20
x*x = 20*5 (by cross-multiplication)
x² = 100
x = √100
x = 10 Ans.

Ans.) The mean proportion of 5, 20 is 10.

Answer 2

The mean proportional between 5 & 20 is 10

Given :

The numbers 5 & 20

To find :

The mean proportional between 5 & 20

Solution :

Step 1 of 2 :

Form the equation

Let x be the mean proportional between 5 & 20

By the given condition

5 : x = x : 20

Step 2 of 2 :

Find the number

$\displaystyle \sf{5 : x = x : 20 }$

$\displaystyle \sf{ \implies \frac{5}{x} = \frac{x}{20} }$

$\displaystyle \sf{ \implies {x}^{2} = 5 \times 20}$

$\displaystyle \sf{ \implies x = \sqrt{5 \times 20}}$

$\displaystyle \sf{ \implies x = \sqrt{100}}$

$\displaystyle \sf{ \implies x = 10}$

The mean proportional between 5 & 20 is 10