Answer:
Area = 420.25 in²
Explanation:
A rectangle is a quadrilateral (has four sides and four angles) with two pairs of opposite and parallel sides. All angles in a rectangle are 90 degrees each. Also, opposite sides are equal.
Let x represent the length of the rectangle and y represent the width of the rectangle. Hence:
Perimeter = 2(length + width)
82 = 2(x + y)
x + y = 41
x = 41 - y
The area of the rectangle (A) = length * width
A = xy
substitute x = 41 - y:
A = (41 - y)y
A = 41y - y²
The maximum area occurs at A' (dA / dy) = 0. Hence:
A' = 41 - 2y
0 = 41 - 2y
2y = 41
y = 20.5 inches
substitute y = 20.5 inches in x = 41 - y:
x = 41 - y = 41 - 20 .5
x = 20.5 inches
The area = xy = 20.5 in * 20.5 in
Area = 420.25 in²