Question

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

Answer 1

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