To find: The function that models the area of rectangle in terms of length of one of its sides. The perimeter of rectangle is 20 ft.

Concept used: Area of rectangle is defined as, ${\displaystyle A=l\cdot b}$ Here, A is area, l is length and b is width. Calculation: Consider the length of one of its sides of rectangle as x. The perimeter of a rectangle is defined as, ${\displaystyle P=2(l+b)}$ Here, P is perimeter. The perimeter of rectangle is given as 20 ft. Substitute 20 for P and x for l in above equation to the value of b. ${\displaystyle 20=2(x+b)}$
${\displaystyle \frac{20}{2}=x+b}$
${\displaystyle 10=x+b}$
${\displaystyle b=10-x}$ Therefore, the value of b is ${\displaystyle (10-x)}$ Substitute x for l and ${\displaystyle 10-x}$ for b in equation to obtain the model that express area of the rectangle ${\displaystyle A=x(10-x)}$
${\displaystyle =10x-x^2}$ Here, x is always greater than zero and less than 10 to define the area therefore the value of x is always lies in between 0 and 10. Conclusion: Thus, the function that models the are of rectangle in terms of length of one of its sides is ${\displaystyle A=10x-x^2}$.