Question

The length and breadth of a rectangle (in cm) are x and y respectively $x\le 30,y\le 20,x\ge 0$ and $y\ge 0$. If a rectangle has a maximum perimeter, then its area is ....... .

Answer 1

The perimeter function is $p=2(x+y)$

$p$ is maximum, when $x=30$ and $y=20$

$⟹p=2\left(50\right)=100$

therefore, the area of the rectangle = $30\times 20=600$ $c{m}^2$