![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjTDW3Bcw9g8JENTCv2ZG2OVUopORGS-rbOwc3pA43ct3TrbnqQXMuWdmBLJd69mbj48wMjxhYJTxfCRpU1ND3CbOWrsMIM8tfpabunZNlowB_S-DkbAiFjUSiDsi3pbMh5T4LtG5rSzYky/s320/RectangleArea.jpg)
The area of a rectangle is always maximized, relative to perimeter, when the rectangle is a square.
To the left is an example where the perimeter of the rectangles remains a constant length of 24 units. The area increases as the sides of the rectangle get closer in length to each other.
![](https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhe1RcWFrXAgqwwLvZZ7-LC8VuuWTodZgLXR2pjwOyBCvR-4Kzjdjrn8kuUICvE3N79_ubP9ueANSmEqPAJclIeP2op9BJ2y6Z15CC9q77oW6ZFGaDWhhMTf5NC5e9D_GdqZ7jMYoNB1PbW/s320/AreaRectangle.jpg)
To the right is an example where the area of the rectangles remains constant at 16 square units. The long thin rectangle has a perimeter of 34 units, the next rectangle has a smaller perimeter of 20 units, but the square's perimeter is just 16 units.
Both examples show that the maximum area of a rectangle, relative to its perimeter, occurs when the rectangle is a square.
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