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Question 323826: Is the area of a rectangle a function of its perimeter?
Can you give me an example including the input and output?
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! No it is not. Say for example you have a perimeter of 14. One way you get a perimeter of 14 is to have side lengths of 2 and 5 (since 2*2+5*2=4+10=14). The area of this 2x5 rectangle is 10 square units. So if we plug in a perimeter of 14, we get an output of 10 (the area)
On the other hand, let's say we now have a 1x6 rectangle (ie width = 1 and length = 6). The perimeter is still 14 units (since 2*1+2*6=2+12=14), but the area is now 1*6=6 square units. So if we plug in 14 (the perimeter) as an input, we get 6 (the area) as an output.
So plugging in 14 gives us either 10 or 6 (and there may be more outputs). So which one is it? Since one input produces more than one output, this means that the area of a rectangle is NOT a function of its perimeter since one perimeter may produce more than one area.
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