What is the largest rectangular area one can enclose with 14 inches of string?

A=w*h

p=2w+2h

if w=x, then h=7-x.

a (x) = x * (7-x)

a (x) = 7x - x^2

to find the largest area we need to derivative a (x):

a' (x) = 7 - 2x = 0 - - > x = 3.5

therefore:

maxArea = a (3.5) = 3.5 * 3.5 = 12.25