Question 132972: Hello, I have a word problem that I just can't solve. I don't have a formula for it. Questions is: The outside of a picture frame measures 14 in by 20 in. 80in squared of the picture shows. Find the thickness of the frame.
I took 14 in by 20 in. =280/ then i divided by 12 inches and came up with 23.33 inches thick? Is this the correct formula?
Thanks,
Kisha Bethea
Answer by solver91311(24713)   (Show Source):
You can put this solution on YOUR website! Your first step was correct, but unnecessary. The total area covered by the frame and the picture inside it is 280 square inches, but we will see that this fact does not enter in to the solution process. I'm not sure what prompted you to divide that number by 12, because that result doesn't mean anything at all in this context.
What we need to know is the dimensions of the picture itself only knowing that the area is 80 sq in. What the problem doesn't say, and what we are going to have to assume in order to solve this, is that the thickness of the frame is uniform all around -- meaning that the thickness is the same on the top, bottom, and both sides. Without this assumption, there are an infinite number of answers and the problem cannot be solved without additional information.
So making the uniform thickness assumption, let's say that this thickness is x.
Since the overall width of the frame is 14 inches, and there are two sides of thickness x to the frame, that means the width of the picture must be 14 - 2x. Likewise, the length dimension of the picture must be 20 - 2x. (See the figure)
We are given that the area of the picture is 80 sq in, and we know that  , we can write:
Now all you need to do is multiply the binomials, put the equation into standard form, and solve it like you would solve any other quadratic equation. I'm going to assume you can take it from here. If you are still having difficulty, write me a note.
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