Astudent has 180 feet of fencing to fence off his rectangular garden. he will use the wall of his house as one side of the garden. (1) write an equation to find the area of the garden (2) what dimensions create the garden with the greatest area: (3) what is the greatest area?

1: because it is a rectangular you can find the area by using this equation: 
A = b*h
2: So you know that 180 feet is for three sides of the garden: 
180 = 2h+b --> b = 180-2h
and you also know that:
A = b*h = (180-2h)*h
If you differentiate (solve A'=0) for this equation, you will find that h=45. 

Therefore b must be equal to 90. 

3: the greatest area is therefore A = 90*45 = 4050

I hope that helped.