Quadratic Relations Thinking Problem

Question

A farmer has 540m of fencing to enclose a rectangular area and divide it into two sections.

a) Write an equation to express the total area enclosed in terms of the width.

b) Determine the dimensions that give the maximum area and calculate the maximum area.

c) Determine the domain and range of this relation.

Answer 1

a) A=270W -(3/2)W^2

b) W=90, L=135 maximizes area= 12,150 m^2

take the derivative of A and set equal to 0

solve for W, then L=(540-3W)/2

c) doman: 0<W<180, range = 0<L<270