## Rectangular problem .

##### This topic has expert replies

- Md.Nazrul Islam
- Senior | Next Rank: 100 Posts
**Posts:**32**Joined:**16 Jul 2011

### GMAT/MBA Expert

- [email protected]
- GMAT Instructor
**Posts:**3835**Joined:**02 Apr 2010**Location:**Milpitas, CA**Thanked**: 1854 times**Followed by:**523 members**GMAT Score:**770

Let us assume that the length = 3n, width = 2n and height = 2nMd.Nazrul Islam wrote:The interior of a rectangular cartoon is designed by a certain manufacturer to have a volume of x cubic feet and a ratio of length to width to height is 3:2:2.In terms of 'x' what is the height of the cartoon in feet .

Then volume = length * width * height = 3n * 2n * 2n = 12(n^3) = x cubic ft

Solving 12(n^3) = x, we get

n^3 = x/12

n = (x/12)^(1/3)

Therefore, height of the carton = 2 * n = [spoiler]2 * (x/12)^(1/3)[/spoiler]

Anurag Mairal, Ph.D., MBA

GMAT Expert, Admissions and Career Guidance

Gurome, Inc.

1-800-566-4043 (USA)

Join Our Facebook Groups

GMAT with Gurome

https://www.facebook.com/groups/272466352793633/

Admissions with Gurome

https://www.facebook.com/groups/461459690536574/

Career Advising with Gurome

https://www.facebook.com/groups/360435787349781/

GMAT Expert, Admissions and Career Guidance

Gurome, Inc.

1-800-566-4043 (USA)

Join Our Facebook Groups

GMAT with Gurome

https://www.facebook.com/groups/272466352793633/

Admissions with Gurome

https://www.facebook.com/groups/461459690536574/

Career Advising with Gurome

https://www.facebook.com/groups/360435787349781/

so, Let the length'l' = 3k, width'w' = 2k and height'h' = 2k

Volume = lxwxh

x = 3k*2k*2k

x = 12k^3

==> k = (x/12)^(1/3)

**so, height 'h' = 2k = 2[(x/12)^(1/3)**

or h = two times the cuberoot of (x/12)

or h = two times the cuberoot of (x/12)