Find a formula for the described function.

Question

A rectangle has perimeter 16 m. Express the area A (in m²) of the rectangle as a function of the length, L, of one of its sides.

then state the domain of A. (Assume the length of the rectangle is longer than its width.)

Answer 1

L+W = 16/2 = 8

A= LW = L(8-L)

A(L) = 8L-L^2 m^2

domain: 0<A<16 meters or (0,16]

domain doesn't include zero, but does include 16

smallest area is nearly 0,

about when Length = 10 bazillion km,

and Width is infinitesmal, a micro micro millimeter

largest area is when L=W=4 and LW =4x4=16