# A rectangular schoolyard is to be fenced in using the wall of the school for one side and 150 meters of fencing for the other three sides. The area A(x) in square meters of the schoolyard is a function of the length x in meters of each of the sides perpendicular to the school wall.

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## Question:

A rectangular schoolyard is to be fenced in using the wall of the school for one side and 150 meters of fencing for the other three sides. The area A(x) in square meters of the schoolyard is a function of the length x in meters of each of the sides perpendicular to the school wall. a. Write an expression for A(x).
b. What is the area of the schoolyard when x=40?
c. What is a reasonable domain for A in this context?

The area of a shape is the amount of space on it.

• The expression for A(x) is • The area when x = 40, is: 2800
• The reasonable domain is: The perimeter of the schoolyard is given as: 150

So, we have: • Where x and y represents the dimension of the schoolyard
• The equation represents the sum of the three sides (because the 4th side is the wall of the school)

Substitute 150 for P Make y the subject The area (A) of a schoolyard is: Substitute  Express as a function The area when x = 40, is:

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Also, we have:

Set to 0 Rewrite as: Divide both sides by -2 So, the reasonable domain is:  