Find the dimensions of the box.

Question

The length of a box is 1 foot greater than its width, and its height is 2 feet less than its width. Find the dimensions of the box given that it's volume is 40 cubic feet.

Answer 1

Volume = L*W*H

 

L=W+1

H=W-2

 

40=L*W*H

 

Let's now substitute in the two equations for L and H to get an equation with one variable:

 

40=(W+1)*W*(W-2)

 

Now we can solve for width; I'll let you do that.

 

Once we know the width, we can find the length and height.

 

 

Answer 2

Let the width of the box be w

length = w + 1

height = w - 2

w * (w+1)*(w-2) = 40

w*(w2 -w -2) = 40

w3 - w2 -2w -40 = 0

you could use factor theorem from here on

which states if f(a) = 0, then f(x-a) is a factor

try 1,2,3, 4. its an iterative process.

W = 4 gives the answer

Hence w = 4, L = 4+1= 5 and H = W-2=2

Checking 2*4*5 = 40 (proven)

Answer 3

We could do this the hard way, or just pick three factors of 40 that match.

 

40 = 8 x 5 = 2 x 4 x 5

 

The box is 4 x 5 x 2.