If X : Y : Z = 1 : 2 : 3 and, X² + Y² + Z² = 224, then what is the value of X + Y + Z?

24

If X : Y : Z = 1 : 2 : 3

X² + Y² + Z² = 224,

then what is the value of X + Y + Z

Let the three numbers = 1m, 2m, 3m

Now according to the question,

(1m)² + (2m)² + (3m)² = 224

= 1m² + 4m² + 9m² = 224

= 14m²  = 224

m² = 16

m = 4

Now, X + Y + Z = 1×4 + 2×4 + 3×4 = 24