## Calculus 8th Edition

$S(x)=x(10-x)=10x-x^{2}$
lets assume the length of one side of the rectangle is x, then the parallel side is x too. so if the perimeter of the rectangle is 20m the sum of the other two parallel sides are equal to $20-x$ therefore one side of them is $\frac{20-2x}{2}=10-x$ because they are equal. therefore the area of the rectangle is one side multiplied by the next side: $S(x)=x(10-x)=10x-x^{2}$