A developer wants to convert a rectangular grassy lot that b

A developer wants to convert a rectangular grassy lot that borders a city street to a parking area. If the developer has 284 feet of fencing to enclose the parking area and does not fence the side along the street, what is the largest area that can be enclosed? What are the dimensions of the lot? (For additional problems like #19, see p. 207 of text, #9, 15.)

Solution

Ans:
Assume that developer fences the three side of a rectangular, we can define dimensions are m and n.
2m + y = 284.
Area is equal to mn.  
Area = mn
As per inequality of arithmetic and geometric means.
(2m+n)/2 mn
284/2 mn
142 mn
142^2 mn
Area 10,082.
The largest area is 10,082 feet sequre.