Maximizing the Area of a Rectangle with Fixed Perimeter

p = 2(w+h) = 2( 10 + 10 ) = 40	a = w × h = 10 × 10 = 100

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,

a=wh

, to

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

2

w

. Elementary calculus shows that this formula is at a maxiumum when

w=10

.