# Maximizing the Area of a Rectangle with Fixed Perimeter

Maximizing the Area of a Rectangle with Fixed Perimeter

Drag the locators to vary the width of the rectangle and see the effect on its area. For a rectangle with a perimeter of 40, the height is always 20 minus the width. This allows you to reduce the formula for the area, , to . Elementary calculus shows that this formula is at a maxiumum when .

a=wh

a=(20-w)w=20w-

2

w

w=10