Fixed Perimeter - Changing Area
There are two sliders below: Slider "a" will change the perimeter of the rectangle. Once you choose a perimeter, use slider "b" to make different rectangles that have the same perimeter.
1) Choose a fixed perimeter of 24 units. Consider all the rectangles that have a perimeter of 24 units. Predict the dimensions of the rectangle with the smallest area. Predict the dimensions of the rectangle with the largest area. 2) Use slider "a" to fix the perimeter of 24 units. Use slider "b" to create the different rectangles with the perimeter of 24 units. Record the length, width, area and perimeter of each rectangle. Compare your data to your prediction in #1. 3) Use the sliders to explore several different perimeters and areas. Come up with a conjecture about the maximum area of a rectangle for any fixed perimeter of a rectangle.