Three numbers are in the ratio 2:3:4. If the sum of their squares is 1856, find the numbers.

• x:y:z = 2a:3a:4a
  (x^2+y^2+z^2) = ((2a)^2+(3a)^2+(4a)^2) = 1856
  (4a^2+9a^2+16a^2 = 1856
  => 29a^2 = 1856
  a^2 = 1856/29=> a^2 = 64
  
  a = 8
  
  x = 2a => 2*8 = 16
  y = 3a => 3*8 = 24
  z = 4a => 4*8 = 32
  
  Ans : x=16, y=24, z=32
• 10 years agoHelpfull: Yes(13) No(1)
• Let the numbers be 2x ,3x, 4x
  Given (2x)^2+(3x)^2+(4x)^2=1856
  => 29x^2=1856
  => x^2=64
  => x=8
  The numbers are 16,24,32
  
• 10 years agoHelpfull: Yes(1) No(1)