Question

The length and width of a rectangle have a sum of 90. What dimensions give the maximum area?

Answer 1

2( l + w) = 90, where l, w are dimensions of the rectangle => l + w = 45;
The maximum area is obtain when l = w;
Then l = w = 45/2 = 22.5

Answer 2

`w-width\\l-length\\\\2w+2l=90\\2l=90-2w\ \ \ \ /:2\\l=45-w\\\\A=wl\to A=w(45-w)=45w-w^2`


`Area\ of\ a\ rectangle\ is\ a\ square\ function.\\The\ maximum\ area\ is\ equal\ to\ the\ y-coordinate\ of\ vertex\\and\`