Question 890284: find the area of its region if the perimeter of a rectangle is 36 cm.
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! If all you are given is the perimeter then you can have several areas, one of which will be the maximum area and one of which will be the minimum area.
I am assuming that the length and width both have to be integers.
If not, then the number of possibilities will be endless.
For Example:
2L + 2W = P
L = length
W = width
P = perimeter = 36
formula becomes:
2L + 2W = 36
solve for L to get:
L = 18 - W
start from a width of 1 and work your way up to get the area and the perimeter each time based on the formula that L = 18 - W
you will get:
W L P A
1 17 36 17
2 16 36 32
3 15 36 45
4 14 36 56
5 13 36 65
6 12 36 72
7 11 36 77
8 10 36 80
9 9 36 81 ***** maximum area when L = W
10 8 36 80
etc...
they repeat from here on, i.e. 8*10 = 10*8, 7*11 = 11*7, etc.
Your maximum area is when L and W are closest in value to each other.
Your minimum area is when L and W are furthest apart in value from each other.
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