question_answer

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

Answer:

Let the numbers be 2x, 3x and 5x

\[\therefore \,\,\,{{\left( 2x \right)}^{2}}+{{\left( 3x \right)}^{2}}+{{\left( 5x \right)}^{2}}=608\]

\[4{{x}^{2}}+9{{x}^{2}}+25{{x}^{2}}=608\]

\[38\text{ }{{x}^{2}}=608\]

\[{{x}^{2}}=\frac{608}{38}=16\]

x = 4

So, the number are 8, 12 and 20.