Question

what is the mean proportion of 4 and 5

Answer 1

x^2=4×5
x^2=20
taking square root on both sides

x=2 under root 5

Answer 2

The mean proportional between 4 and 5 is 2√5

Given :

The numbers 4 and 5

To find :

The mean proportional between 4 and 5

Solution :

Step 1 of 2 :

Form the equation

Let x be the mean proportional between 4 and 5

By the given condition

4 : x = x : 5

Step 2 of 2 :

Find the number

$\displaystyle \sf{4 : x = x : 5 }$

$\displaystyle \sf{ \implies \frac{4}{x} = \frac{x}{5} }$

$\displaystyle \sf{ \implies {x}^{2} = 4 \times 5}$

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

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

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

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

$\displaystyle \sf{ \implies x = 2 \sqrt{5} }$

Hence mean proportional between 4 and 5 is 2√5

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