Question

A rectangle has a perimeter of 20 ft. Find a function that models its area A in terms of the length x of one of its sides.

1. Latifah
The function that models the area A of the rectangle is A=10H-H².

### Rectangles

The rectangle is a quadrilateral.  The classification for quadrilaterals is given by the length of sides and angles. For a rectangle,  the opposite sides are equal and parallel and their interior angles are equal to 90°.
A rectangle is a quadrilateral that has 4 sides called: base and height. Due to its characteristics, the rectangle presents two bases (B) and two heights (H).
The perimeter of a geometric figure is the sum of its sides. Thus, for a rectangle, the perimeter can be calculated from equation 2B+2H.
The area of a rectangle can be found for the formula : B*H, where B = base and H =height.
For this question:
Perimeter = 20 ft
From the perimeter, you have the following equation:
2B+2H=P
2B+2H=20
Then,
2B=20-2H , dividing all terms by 2
B=10-H
Like the area (A) is given by B*H, you will have:
A=B*H
A=(10-H)*H
A=10H-H²