22. many rectangles have a perimeter of 81 feet. find the dimensions for the one with the maximum enclosed area. a) 20.25 feet × 20.25 feet b) 11 feet × 29.5 feet c) 9 feet × 9 feet d) 17.5 feet × 23 feet

Let
x> the length of the rectangle
y> the width of the rectangle

we know that
perimeter of rectangle=2*[x+y]
area of rectangle=x*y
P=81 ft
so
81=2*[x+y]> 40.5=[x+y]

case A) 20.25 feet × 20.25 feet
P=2*[20.25+20.25]> 81 ft> the perimeter is ok
A=20.25*20.25> 410.06 ft²

case B) 11 feet × 29.5 feet
P=2*[11+29.5]> 81 ft> the perimeter is ok
A=11*29.5> 324.5 ft²

case C) 9 feet × 9 feet
P=2*[9+9]> 36 ft> the perimeter is not 81
A=9*9> 81 ft²

case D) 17.5 feet × 23 feet
P=2*[17.5+23]> 81 ft> the perimeter is ok
A=17.5*23> 402.5 ft²

the answer is
case A) 20.25 feet × 20.25 feet