SOLUTION: I have a hard time with word problems. Could you please help me get started on this? I don't want the answer, just a good jumpstart on how to begin. The volume of the box is r

Question 105763This question is from textbook Beginning Algebra
: I have a hard time with word problems. Could you please help me get started on this? I don't want the answer, just a good jumpstart on how to begin.
The volume of the box is represented by (x^2+5x+6)(x+5). Find the polynomial that represents the area of the bottom of the box.
It also has the equation x+2 next to a picture of the box.
I think that the formula for area is:
A=2LW+2LH+2LW
A=Area
L=length
W=width
H=height
I am really unsure on how to begin this. Again, if you can get me started in the right direction, I would really appreciate the help. This question is from textbook Beginning Algebra

Answer by bucky(2189) (Show Source): You can put this solution on YOUR website!
Without seeing the picture of the box that is shown, it's a little difficult to come up
with the method you need to use.
.
First, let's clear up some definitions. The volume of a box is found by multiplying
the length of the bottom times the width of the bottom times the height of the box.
Therefore, the equation for the volume of the box is V = L*W*H. You are told that
the volume of the box in this problem is (x^2 + 5x + 6)(x + 5). From this you can gather
that x + 5 is one of the sides of the box. And you can also gather that (x^2 + 5x + 6)
is the product of the other two sides of the box.
.
Here is a thought that may help. Notice that the polynomial x^2 + 5x + 6 can be factored
into the product (x + 2)*(x + 3)
.
From this you can say that the dimensions of the box are x + 2 by x + 3 by x + 5
.
The question now is which of these three dimensions is the length of the bottom, which is
the width of the bottom, and which is the height of the box.
.
Next let's clarify how you find the area of the bottom of the box. The area of the box's
bottom is found my multiplying the two sides of the bottom. One of the sides of the bottom
should be the length and the other side the width. So the area of the bottom of the box
is given by the equation A = L*W
.
The longest of the three sides is x + 5. I'm going to guess that it is the length of the
bottom. And I'm also going to guess that the x + 2 shown on the picture is the side that
is the height of the box. This would mean that the width of the bottom of the box is
x + 3. The area of the bottom of the box is the product of the length of the bottom
times the width of the bottom. Therefore, if my guesses are correct, the area of the bottom
of the box is given by the product of x + 3 and x + 5. You can multiply that out to find
the answer to your problem.
.
If my guesses are wrong, you will need to identify which of the three sides is the height
of the box. Then multiply the remaining two sides together and you should have the answer
to your problem.
.
Hope this is enough of a jump start to allow you to work the problem to an answer
and what's even more important ... to understand what you are doing.
.

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