Question

Question 130

Solve the following question:

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

Answer 1

Let the three numbers be 2x, 3x and 5x respectively.
According to the question,
$(2x{)}^2+(3x{)}^2+(5x{)}^2=608$ [given]
$\Rightarrow 4x^2+9x^2+25x^2=608$
$\Rightarrow 38x^2=608$
$\Rightarrow x^2=\frac{608}{38}$
$\Rightarrow x^2=16=(4{)}^2$
$\therefore x=4$
Hence, the numbers are $2\times 4,3\times 4,5\times 4$ i.e. 8, 12, and 20.