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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

Respuesta :

calculista
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

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