Question

find three positive numbers in the ratio 2:3:5, the sum of whose squares is 950.

Answer 1

Ratio = 2 : 3 : 5

Define x:

Ratio = 2 : 3 : 5

Let x be the constant ratio

Ratio = 2x : 3x : 5x

Form equation:

The sum of their squares is 950

(2x)² + (3x)² + (5x)² = 950

4x² + 9x² + 25x² = 950

38x² = 950

x² = 950 ÷ 38

x² = 25

x = √25

x = 5

Find the numbers:

2x = 2(5) = 10

3x = 3(5) = 15

5x = 5(5) = 25

Answer: The numbers are 10, 15 and 25

Answer 2

let the common multiple be x
then according to given condition

(2x)2+(3x)2+(5x)2=950
4x2+9x2+25x2=950
38x2=950
x2=25
x=5

2x=10
3x=15
5x=25
the three numbers are 10,15,25