Question 51780
2l + 2w = 300
l = (300 - 2w) / 2
l = 150 - w
A = w*l
A = w*(150 - w)
{{{A = 150w - w^2}}}
Let's say w = 75 (square patio)
{{{A = 150*75 - 75^2}}}
{{{A = 11250 - 5625}}}
{{{A = 5625}}}
What if w = 74?
{{{A = 150*74 - 74^2}}}
{{{A = 11100 - 5476}}}
{{{A = 5624}}}
What if w = 76?
{{{A = 150*76 - 76^2}}}
{{{A = 11400 - 5776}}}
{{{A = 5624}}}
So, if I go up a little from w = 75 or down
a little from w = 75, A goes down.
w = 75 and l = 75 gives the max area