If ` x , 12 , y, 27` are in continued proportion, then find the positive value of x and y .

Explanation

`:' x/12 = 12/y " or, " xy = 144` …………. (1)
Again, 12 y, 27 are in continued proportion,
` :. 12/y = y/27 " or, " y^(2) = 12 = 12 xx 27 `.
or, ` y^(2) = 324 " or, " y = sqrt(324) " or, " y = sqrt( 324) = pm 18` .
` :' y gt 0, :. y = 18 ` .
Now , from (1) We get , ` x xx 18 = 144 " or, " x = 144/18 = 8`. ,brgt ` :. x = 8 " and " y = 18`.
Aliter : Since x, 12, y, 27 are in continued proportion.
` :. x/12 = 12/y = y/27`
Now, ` x/12 = 12/y rArr xy = 144 ` ................ (1)
Again, ` 12/y = y/27 " or, " y^(2) = 324 " or, " y = sqrt(324) = pm 18`.
But ` y gt 0 , :. y = 18` .
`:. ` from (1) we get, ` x xx 18 = 144 " or, " x = 144/18 = 8`.
Hence ` x = 8 " and " y = 18` .