# How do you find the maximum area of a rectangle whose perimeter is 100cm?

Refer to explanation

#### Explanation:

Let L= length of rectangle
and W=width of rectangle

Hence perimeter is $P = 2 \cdot \left(L + W\right) \implies L + W = 50 \implies W = 50 - L$

The area of rectangle is $A = L \cdot W \implies A = L \cdot \left(50 - L\right)$

The first derivative gives

$\frac{\mathrm{dA}}{\mathrm{dL}} = 50 - 2 \cdot L \implies \frac{\mathrm{dA}}{\mathrm{dL}} = 0 \implies L = 25$

Hence for $W = L = 25$ we have the maximum area which is

$A = L \cdot W = 25 \cdot 25 = 625$