Math Question
![A school wishes to form three sides of a rectangular playground using 240 meters of fencing. The playground borders the school building, so the fourth side does not need fencing.
As shown below, one of the sides has length \( x \) (in meters).
Side along school building
\( x \)
(a) Find a function that gives the area \( A(x) \) of the playground (in square meters) in terms of \( x \).
\[
A(x)=\prod
\]
(b) What side length \( x \) gives the maximum area that the playground can have?
Side length \( x \) : meters
(c) What is the maximum area that the playground can have?
Maximum area: [square meters](https://d3hlidq5bf9vg0.cloudfront.net/app-server-student/2022/4/24/0813e3da-99e0-47a5-a832-87a67f8de9e4.png "A school wishes to form three sides of a rectangular playground using 240 meters of fencing. The playground borders the school building, so the fourth side does not need fencing.
As shown below, one of the sides has length \( x \) (in meters).
Side along school building
\( x \)
(a) Find a function that gives the area \( A(x) \) of the playground (in square meters) in terms of \( x \).
\[
A(x)=\prod
\]
(b) What side length \( x \) gives the maximum area that the playground can have?
Side length \( x \) : meters
(c) What is the maximum area that the playground can have?
Maximum area: [square meters")
Solution
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