Question

Suppose a farmer wants to fence off a rectangular area with three sides of a rectangle, using a river as the fourth side. He has 100 yards of fence to use. Let x denote the length of the side of the rectangle parallel to the river. Find a formula for the function A(x) that gives the area as a function of x. What is the domain of this function based on the formula and what is it based on the context of the problem?

Answer 1

A = Area
x = Side Parallel to the river.

$a = (\frac{x}{2}) \times x$

Which in your context results to:

$x = 100 \div 2$
$1250 = ( \frac{50}{2} ) \times 50$

Area = 1250 yards squared