Question

Find the mean proportional bwtween 1.5 and 13.5
and the anser in the back of my book says the awnser is ;4.5 i just need to know how to get 4.5 thank you if you explain this to me

Answer 1

Answer:

The answer in book is correct. 1.5:x::x:13.5 where x is mean proportional,and 1.5 and 13.5 are called extremes. As it is in proportional x*x=1.5*13.5 , so x²=1.5×13.5

x=root of 20.25 i.e 4.5

Answer 2

The mean proportional between 1.5 and 13.5 is 4.5

Given :

The numbers 1.5 and 13.5

To find :

The mean proportional between 1.5 and 13.5

Solution :

Step 1 of 2 :

Form the equation

Let x be the mean proportional between 1.5 and 13.5

By the given condition

1.5 : x = x : 13.5

Step 2 of 2 :

Find the number

$\displaystyle \sf{1.5 : x = x : 13.5 }$

$\displaystyle \sf{ \implies \frac{1.5}{x} = \frac{x}{13.5} }$

$\displaystyle \sf{ \implies {x}^{2} = 1.5 \times 13.5}$

$\displaystyle \sf{ \implies x = \sqrt{1.5 \times 13.5}}$

$\displaystyle \sf{ \implies x = \sqrt{ \frac{15}{10 } \times \frac{135}{10} }}$

$\displaystyle \sf{ \implies x = \sqrt{ \frac{15 \times 135}{10 \times 10} }}$

$\displaystyle \sf{ \implies x = \sqrt{ \frac{3 \times 5 \times 3 \times 3 \times 3 \times 5}{10 \times 10} }}$

$\displaystyle \sf{ \implies x = \sqrt{ \frac{ {3}^{2} \times {3}^{2} \times {5}^{2} }{ {10}^{2} } }}$

$\displaystyle \sf{ \implies x = \frac{3 \times 3 \times 5}{10} }$

$\displaystyle \sf{ \implies x = \frac{45}{10} }$

$\displaystyle \sf{ \implies x = 4.5}$

Hence the mean proportional between 1.5 and 13.5 is 4.5

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