Question 1022998: Karl is putting a frame around a rectangular photograph. The photograph is 12 inches long and 10 inches wide, and the frame is the same width all the way around. What will be the area of the framed photograph?
Found 3 solutions by Fombitz, DrSteve, ikleyn:
Answer by Fombitz(32388)   (Show Source):
Answer by DrSteve(7)  (Show Source):
You can put this solution on YOUR website! I hate to disagree, but there IS a solution, albeit a POLYNOMIAL EXPRESSION, which is what the problem is seeking.
The "frame is the same width all the way around" is another way to say that the frame is square.
So we're looking for a polynomial expression that gives the area of the framed photograph given that the frame is square and the photograph is 12 inches long and 10 inches wide.
If it were a 12x12 photograph, we'd just have to add some constant to the sides to get the frame size, let's call it "x".
So one side would be 12+2x (remember we're adding "x" to each side of the photograph), and the area would be (12+2x) * (12+2x), or  .
However, one side is only 10 inches, so the formula for that length would be:
10+(2x+12).
BUT NOTICE! Remember, this is a SQUARE picture frame so we only need one side. ALSO,
10+(2x+12)=12+2x which is the same formula for the other side, again confirming that this is a square that we're dealing with.
SO
just square one of the sides which gives:
which is your answer.
By the way, you can check this answer!
Let's do a 1 inch border on the 12 inch side, creating a 14 inch square frame.
The 10 inch side would be 10 + 2*1 + 2 or 14 inches as well (see above...just checking that our math is right, though we really don't need it.)
Using the polynomial above, we would get:
144 + 48 + 4 = 196
simply squaring 14 = 196
therefore our polynomial expression works!
HAVE FUN WITH MATH! :-)
Answer by ikleyn(52754)  (Show Source):
You can put this solution on YOUR website! .
Karl is putting a frame around a rectangular photograph. The photograph is 12 inches long and 10 inches wide,
and the frame is the same width all the way around. What will be the area of the framed photograph?
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The area of the framed photograph will be (12+2x)*(10+2x) squared inches,
where x is an unknown uniform width of the frame all way around.
Since the value of "x" is not given in the condition, we can not go further and calculate the area as the number.
In this sense, I agree with @Fombitz and do not agree with @DrSteve.
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Since something happened with the post by @Fombitz, I extracted it from the archive, copied and pasted below:
Without the width of the frame, you can't have a solution.
Please repost.
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On how such problems are usually presented (and solved), see the lesson
- Problems on the area and the dimensions of a rectangle surrounded by a strip
in this site.
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In the commonly accepted word usage, the width of the frame is the width of the strip around the picture,
and IS NOT one of the outer/exterior dimensions of the frame.
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