Spring Garden

Each spring, a 12 meter by 12 meter garden has its length increased by 2 meters but its with decreased by 50 centimeters. What will be the maximum attainable area of the garden?
Source: NCTM Mathematics Teacher, October 2006

Solution
Area in square meters per each year starting from year 0
0\!:\!(12)(12)
1\!:\!(12+2)(12-.5)=(12+1(2)(12-1(.5)
2\!:\!(12+2+2)(12-.5-.5)=(12+2(2))(12-2(.5)
3\!:\!(12+2+2+2)(12-.5-.5-.5)=(12+3(2))(12-3(.5))
\cdots
In general in year x, the area equals
(12+x(2))(12-x(.5))=-x^2+18x+144
The graph of this quadratic expresion is shown below

image
The area reaches a maximum of 225 square meters in year x=9.

Answer: 225 square meters

Advertisements

About mvtrinh

Retired high school math teacher.
This entry was posted in Problem solving and tagged , , , , . Bookmark the permalink.

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s