# A rectangle has perimeter 20 m. Express the area

#### Solution:

Let L represent the length and W represent the width of the rectangle. Therefore, the perimeter is $2L+2W = 20m$ and area is $A=LW$.

Solve the first equation so that W is isolated.

$W=\frac{20-2L}{2}=10-L$.

Therefore, if we write area as a function of length, then

$A(L)=L(10-L)=10L-L^{2}$

We know that the lengths must be positive, so the domain of A is 0<L<10. Furthermore, because length is usually longer than the width, we can restrict it so that length must always be longer than width. Then the domain of A is 5<L<10.