rectangular pen perimeter = 60 ft determine equation to model area of pen graph relationship between length of side and area of the rectangle
graph the relationship between the length of a side and the area of the rectangle
A good place to start is always determining what the equation is actually communicating. In this case, there is a rectangle with a perimeter of 60ft and we are asked to find an equation that represents all possible areas of the rectangle. Defining the rectangle with sides x and y, the area of the rectangle can be represented with the formula:
Where A represents area. Unfortunately there are too many variable in this equation to be of much use. We need to look for more information. We do have a constant perimeter of 60ft, this allows for the formula
Using this formula, we can solve for either x or y. Solving for y results in:
Inserting this value of y into the area formula:
x*(30-x)=A OR A=-x^2+30*x
This formula can be graphed, resulting in a concave down parabola, crossing the x axis at (0,0) and (0,30) and a maximum at (15,225).