Question

3 numbers are in the ratio 4:5:3, the sum of whose squares is 1250.Find the numbers.

Answer 1

lets take three numbers in ratio 4:5:3be 4k,5k,3k. Sum of squares of these numbers=
$16 {k}^{2} + 25 {k}^{2} + 9 {k}^{2} = 50 {k}^{2}$
=> 1250=
$50 {k}^{2}$
=>25=
${k}^{2}$
=>k=5 or-5(Not possible)
=>numbers are 20,25 and 15 respectively.