A rectangular box of volume x has width, depth and height in the ratio of 2:3:3 (in that order). What is the width as a function of x? Select the correct option
A) (2x/12)^(1/2)
B) (x/2)^(1/2)
C) (x/3)^(1/2)
D) (2x/9)^(1/2)
E) (x)^(1/2)
We are given width = 2, depth = 3, height = 3   Then Volume x = Width x Depth x Height = 2*3*3= 
<gadget id="calculator">2*3*3</gadget>
<output>18</output>
18   i.e. x= 18   i.e. The correct option should result in 2 on substituting the value of x=18   Checking options with x=18   A) (2x/12)^(1/2) = (2*18/12)^(1/2) = 3^(1/2) INCORRECT ANSWER   B) (x/2)^(1/2) = (18/2)^(1/2) = 9^(1/2) = 3 INCORRECT ANSWER   C) (x/3)^(1/2) = (18/3)^(1/2) INCORRECT ANSWER   (2x/9)^(1/2)) (2x/9)^(1/2) = (2*18/9)^(1/2) = 4^(1/2) = 2 CORRECT ANSWER   E) (x)^(1/2) = (18)^(1/2) INCORRECT ANSWER   Answer: Option (2x/9)^(1/2)
<result>D</result>
A rectangular box of volume x has width, depth and height in the ratio of 2:3:3 (in that order). What is the width as a function of x?