The dimensions of a shed has the length 2m longer than the width and the height 2m less than the width. If the volume of the shed is 105 m^3 , find the dimensions.

Answer 1

Greeting Fouzan A. Hope you had a terrific holiday season and Happy New Year. You have a terrific question and is one of the basic concepts of Algebra. If you are able to conquer this skill it will allow you to advance your understanding of Algebra...finding a solution when some of the information is not always known or is dependent on some portion of the information provide to you.

I will help you set up the problem, however, I won't give you the answer...that is your challenge...because when it come to this kind of a problem on a test, I won't be there to help you with the answer, however if you set up the problem like I'll show you then you'll be a champ and answering this kind of question. Okay...here goes.

So let's take your problem...it gives you some information and asks you to solve a question. In Algebra we deal with what we know and what we don't know...the knows and the unknowns.

So...what we know is some information about the dimensions of a shed [which is basically a cube] as well as the volume of the shed and what we don't know [or asked to find] are the actual dimensions...the length, width and height of the shed.

You will have to know a few things. What does volume mean?

How do you find the volume of a 3 dimensional object, a cube?

If you can answer these questions...then the rest isn't too difficult.

Answer 2

While we can clearly see that 3*5*7 = 105 and meets the conditions of the problem, if we want to work with the problem wording as closely as possible, since length and height are given in terms of width,

l = w + 2

h = w - 2

lwh = 105

(w+2)w(w-2) = 105

w^3 - 4w = 105

w^3 - 4w - 105 = 0

(w - 5)(w^2 + 5w + 21) = 0

w = 5 (other 2 roots are irrational)

l = w + 2 = 7

h = w - 2 = 3