Question

Find three numbers in the ratio $2:3:5$, the sum of whose squares is $608$.

Answer 1

Step 1: Evaluate the equation

The given ratio is $2:3:5$.

Let us assume the three numbers be $2n,3n$ and $5n$.

Given that sum of squares of three numbers is $608$.

$\therefore {\left(2n\right)}^2+{\left(3n\right)}^2+{\left(5n\right)}^2=608$

$\Rightarrow$ $4n^2+9n^2+25n^2=608$

$\Rightarrow$ $38n^2=608$

$\Rightarrow$ $n^2=\frac{608}{38}$

$\Rightarrow$ $n^2=16$

$\Rightarrow$ $n=4$

Step 2: Calculate the required numbers

Therefore, the numbers are,

$2n=2\times 4=8$

$3n=3\times 4=12$

$5n=5\times 4=20$

Hence, the required numbers are $8,12,$ and $20$.