To state: A quadratic function to represent the area of all rectangles with a perimeter of 36 ft. Then graph the function and describe the rectangle that has the largest area.
The quadratic function that represents the area of all rectangles is
Given information:
The given perimeter of a rectangle is 36ft.
Explanation:
Let’s assume x as the length of the rectangle and y as the width of the rectangle.
Then the perimeter of the rectangle is:
Now the area of the rectangle is:
Now plot the function
This function will have value 0 at,
The resultant graph looks like a parabola and it has its maximum at
Then,
Now the maximum area will be:
Therefore, the maximum area is 81 square feet.
Chapter 4 Solutions
High School Math 2015 Common Core Algebra 2 Student Edition Grades 10/11
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