You are building a backyard for a school. The yard will be 3 sided as it will be built against the side of the house. You have 1800m of fencing to build the backyard.

Question

Find the dimensions so that the total enclosed area is a maximum.

Answer 1

Set up the problem so that y= side perpendicular to the house and x=side parallel to the house. So the perimeter = x + 2y = 1800 and x= 1800 - 2y. the area is A= xy = ( 1800 - 2Y )y. To find the maximum dimensions plot y vs the Area in a table as follows:

y 300 400 450 500

Area 360000 400000 405000 400000 Hence the largest area is when y= 450m and x= 900m.