\(\)

Mascarfi wrote:

A rectangular box of volume x has width, depth and height in the ratio of 3:2:2 (in this order). What is the height in function of x?

A) (x/12)^(1/3)

B) (x/6)^(1/3)

C) (x/4)^(1/3)

D) (2x/3)^(1/3)

E) (x)^(1/3)

Method 1:Use easy numbers as all the options have x as the variable. let x = 12 ( a good number as the ratio is 3:2:2)

Thus x = volume = LWH ---> 12 = 3*2*H ---> H = 2 units.

Now plug in x =12 and see which option give you a value of 2 . Only D gives you a value of 2 and is thus the correct answer.

Method 2:Alternately, you can use proportions to calculate the height. Let y be the common factor for length, width and height. Thus L=3y, W=2y , H = 2y

Thus, 3y*2y*2y = x ---> \(12y^3 = x\)--->\(y = (x/12)^{1/3}\) and

\(height = 2y= 2 (x/12)^{1/3} = (8x/12)^{1/3} = (2x/3)^{1/3}\) , D is the correct answer.