# What rectangle dimensions gives the largest possible area given the perimeter of a rectangle is 300ft?

Mar 20, 2016

$75 \text{ft" xx 75"ft}$

#### Explanation:

Suppose the length of one side of the rectange is $t$ feet.

Then the rectangle area is:

$t \cdot \left(150 - t\right) = 150 t - {t}^{2} = {75}^{2} - {\left(t - 75\right)}^{2}$

which takes it maximum value when ${\left(t - 75\right)}^{2} = 0$, i.e. when $t = 75$