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Find three number in the ratio of $2:3:4$, the sum of whose square is $725$.
Given: Three number are in the ratio of $2:3:4$, the sum of whose square is $725$.
To do: To find the numbers.
Solution:
Ratio of the numbers$=2:3:4$
Let $2x,\ 3x$ and $4x$ be the three numbers in the given given ratio.
As given, sum of the squares of the numbers is $725$.
$\Rightarrow ( 2x)^2+( 3x)^2+( 4x)^2=725$
$\Rightarrow 4x^2+9x^2+16x^2=725$
$\Rightarrow 29x^2=725$
$\Rightarrow x^2=\frac{725}{29}$
$\Rightarrow x^2=25$
$\Rightarrow x=\sqrt{25}$
$\Rightarrow x=5$
Now, put the value of $x$ in $2x,\ 3x$ and $4x$,
$2x=2\times5=10$
$3x=3\times5=15$
$4x=4\times5=20$
Therefore, the numbers are $10,\ 15,\ 20$.
Updated on: 10-Oct-2022
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