Question

The sum of the squares of 3 numbers which are in the ratio 3:4:5 is 800.Find the numbers

Answer 1

$$\begin{gathered} \mathrm{Let}\mathrm{the}\mathrm{first}\mathrm{number}=3x \\ \mathrm{then}\mathrm{second}\mathrm{number}=4x \\ \mathrm{third}\mathrm{number}=5x \\ \mathrm{Now},\mathrm{according}\mathrm{to}\mathrm{question}, \\ {\left(3x\right)}^2+{\left(4x\right)}^2+{\left(5x\right)}^2=800 \\ \Rightarrow 9x^2+16x^2+25x^2=800 \\ \Rightarrow 50x^2=800 \\ \Rightarrow x^2=16 \\ \Rightarrow x=4 \\ \mathrm{Now},\mathrm{first}\mathrm{number}=3\times 4=12 \\ \mathrm{second}\mathrm{number}=4\times 4=16 \\ \mathrm{third}\mathrm{number}=5\times 4=20 \end{gathered}$$