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 feetB) 11 feet × 29.5 feetC) 9 feet × 9 feetD) 17.5 feet × 23 feet
Accepted Solution
A:
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