B) Find the dimensions of the rectangle with perimeter 64 inches that has maximum area, and then find the maximum area.

Question

L=_____, W=_____, Maximum area=____

Answer 1

P = 2*(L+w)

64 = 2*(L+w)

32 = L + w

Area = L * w = (32 - w)*w <--- area is quadratic function of width

= -w^2 + 32*w

A=-1 B=32

max occurs at -b/(2a) = -32/(2* -1) = -32/-2 = 16

Max area is 16*16 = 256