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

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.

RELATED QUESTIONS
Mr.Larsen put a fence around the sides of a rectangular piece of property he owns. If the (answered by Boreal)

"You have a rectangular piece of property that has a width of 30 � feet and a length of... (answered by edjones)

If someone drove a toatle of 504 miles in 9 hours what would there average rate of speed... (answered by Alan3354,Hasdrubal)

I need all of these questions solved please I need help!!! 1.Find the area under the... (answered by ikleyn,Boreal)

Hello, this is an example problem that we were given to solve and i don't understand if... (answered by rfer)

A garden area is 30 ft long and 20 ft wide. A path of uniform width is set around the... (answered by Paul)

Assume that we have two events, A and B, that are mutually exclusive. Assume further that (answered by ikleyn)

If one 30 - 60 - 90 triangle has a short leg 8 inches long, and another has a short leg... (answered by ewatrrr)

"How can I determine the range of possible values of the fourth side of a quadrilateral... (answered by MathLover1,richard1234)