# 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 $10,\ 15,\ 20$.

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