Answer
Verified
396.3k+ views
Hint: In algebra, a mean proportional is a number that comes between two numbers . We used a mean proportional formula which is $\sqrt {ab} = $mean proportional. And the formula of third proportional $ac = {b^2}$.
Complete step-by-step answer:
Mean proportional of two number is given in the question but numbers are not
So first we have to let a, b are the required numbers.
Formula of mean proportional
$\sqrt {ab} = $mean proportional
$\sqrt {ab} = 28$
Now take the square both side
${(\sqrt {ab} )^2} = {28^2}$
$ab = 28.28$
$ab = 784$
So we can find the value of number a
$a = \dfrac{{784}}{b}$ ……… equation (1)
We have the third proportional given in the question that is 224
The formula of third proportional
$ac = {b^2}$
$c = \dfrac{{{b^2}}}{a}$
Put the values
Here c is the third proportional
$224 = \dfrac{{{b^2}}}{a}$
Now put the value of a
$224 = \dfrac{{{b^2}}}{{\dfrac{{784}}{b}}}$
Simplifying the equation
$224 = {b^2}.\dfrac{b}{{784}}$
Multiply the R.H.S
$224 = \dfrac{{{b^3}}}{{784}}$
Apply the cross-multiplication method
${b^3} = 224.784$
${b^3} = $175616
$b{ = ^3}\sqrt {175616} $
$b = 56$
So here we the second number
We can find the first number a with the help of equation (1)
$a = \dfrac{{784}}{b}$
$a = \dfrac{{784}}{{56}}$
$a = 14$
Hence, we have both the numbers
First is 14 and the second number is 56.
Note: In this type of question the most important point is calculation, always do the calculation carefully. We can check our answer by using a mean proportional method
Mean proportional =$\sqrt {a.b} $
We have a = 14
And b = 56
After putting the values, we get
= $\sqrt {14.56} $
$ = \sqrt {784} $
$ = 28$
So here we get mean proportional that is already given in the question
Our answer is correct by alternative checking method.
Complete step-by-step answer:
Mean proportional of two number is given in the question but numbers are not
So first we have to let a, b are the required numbers.
Formula of mean proportional
$\sqrt {ab} = $mean proportional
$\sqrt {ab} = 28$
Now take the square both side
${(\sqrt {ab} )^2} = {28^2}$
$ab = 28.28$
$ab = 784$
So we can find the value of number a
$a = \dfrac{{784}}{b}$ ……… equation (1)
We have the third proportional given in the question that is 224
The formula of third proportional
$ac = {b^2}$
$c = \dfrac{{{b^2}}}{a}$
Put the values
Here c is the third proportional
$224 = \dfrac{{{b^2}}}{a}$
Now put the value of a
$224 = \dfrac{{{b^2}}}{{\dfrac{{784}}{b}}}$
Simplifying the equation
$224 = {b^2}.\dfrac{b}{{784}}$
Multiply the R.H.S
$224 = \dfrac{{{b^3}}}{{784}}$
Apply the cross-multiplication method
${b^3} = 224.784$
${b^3} = $175616
$b{ = ^3}\sqrt {175616} $
$b = 56$
So here we the second number
We can find the first number a with the help of equation (1)
$a = \dfrac{{784}}{b}$
$a = \dfrac{{784}}{{56}}$
$a = 14$
Hence, we have both the numbers
First is 14 and the second number is 56.
Note: In this type of question the most important point is calculation, always do the calculation carefully. We can check our answer by using a mean proportional method
Mean proportional =$\sqrt {a.b} $
We have a = 14
And b = 56
After putting the values, we get
= $\sqrt {14.56} $
$ = \sqrt {784} $
$ = 28$
So here we get mean proportional that is already given in the question
Our answer is correct by alternative checking method.
Recently Updated Pages
Assertion The resistivity of a semiconductor increases class 13 physics CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
How do you arrange NH4 + BF3 H2O C2H2 in increasing class 11 chemistry CBSE
Is H mCT and q mCT the same thing If so which is more class 11 chemistry CBSE
What are the possible quantum number for the last outermost class 11 chemistry CBSE
Is C2 paramagnetic or diamagnetic class 11 chemistry CBSE
Trending doubts
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Difference Between Plant Cell and Animal Cell
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
What organs are located on the left side of your body class 11 biology CBSE
Write an application to the principal requesting five class 10 english CBSE
What is the type of food and mode of feeding of the class 11 biology CBSE
Name 10 Living and Non living things class 9 biology CBSE