Question

A farmer has 100 m of fencing to enclose a rectangular pen.

Use the equation: A(w) = 50w – w2

What is the greatest rectangular area that the farmer can enclose with 100 m of fencing?

Answer 1

The greatest rectangular area that the farmer can enclose with 100 m of fencing is 625m2.

Answer 2

A(w) = 50w-w^2

rewrite it as y = -w^2 +50w

using quadratic formula y = ax^2 +bx +c
a would equal -1, b = 50 and c = 0

find the axis of symmetry using x = -b/2(a)
so x = -50 / 2(-1) = -50/-2 = 25

so the width = 25 m

the greatest area is a square, so area = 25^2 = 625 square meters