Question

Three no are in the ratio 2 3 4 the sum of the square of the no is 116

Answer 1

given, three numbers are in ratio 2 : 3 : 4.

let x is proportionality constant.

then, three numbers are ; 2x , 3x and 4x respectively.

a/c to question,

sum of the square of numbers = 116

or, (2x)² + (3x)² + (4x)² = 116

or, 4x² + 9x² + 16x² = 116

or, 29x² = 116

or, x² = 4 ⇒x = 2

so, first number = 2x = 2 × 2 = 4

2nd number = 3x = 3 × 2 = 6

3rd number = 4x = 4 × 2 = 8