SOLUTION: If we are given that the distance around a piece of property is 30 miles what would be the range of possible areas that the property could have- now also given that the shape is a
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Question 446949: If we are given that the distance around a piece of property is 30 miles what would be the range of possible areas that the property could have- now also given that the shape is a rectangle what would be the possible areas that the property could have Answer by htmentor(1343) (Show Source):
You can put this solution on YOUR website! If the property has a rectangular shape then for the perimeter and area we can write:
2l + 2w = 30 -> l + w = 15
l*w = A
where l=length, w=width
We can express w in terms of l:
w = 15 - l
Then A = l(15 - l)
We assume that the lengths of the sides are made up of whole numbers.
The range of areas will be obtained if we let l range from 1 to 7.
Note that we can stop at 7 since 8*7 = 7*8, 9*6 = 6*9, etc.
For l = 1, A = (1)(14) = 14
For l = 7, A = (7)(8) = 56
So the range of areas is 14 to 56 sq. mi.
The graph of the area as a function of the length is shown below.
