SOLUTION: Several rectangles with a perimeter of 14 cm have widths and lengths that are a natural number of centimeters. How many different areas are possible for these rectangles?

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Question 1061802: Several rectangles with a perimeter of 14 cm have widths and lengths that are a natural number of centimeters. How many different areas are possible for these rectangles?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
perimeter=2%28length+%2Bwidth%29
If 2%28length+%2Bwidth%29=14 , length%2Bwidth=14%2F2--->length%2Bwidth=7 .
How many ways can we make length%2Bwidth=7 with natural numbers (the positive integers we use to count)?
Let us count the ways, starting with width=1 and going wider:
system%28width=1%2Clength=7-1=6%29 ---> area=6%2A1=6
system%28width=2%2Clength=7-2=5%29 ---> area=5%2A2=10
system%28width=3%2Clength=7-3=4%29 ---> area=4%2A3=12
We cannot say system%28width=4%2Clength=7-4=3%29 is an option,
because the way we define those words width%3C=length ,
and anyway, we would find the same area: area=3%2A4=12 .
So, there are highlight%283%29 different possible areas.