Today we'll discover something amazing about rectangles! When we have a rope of fixed length, we can make different rectangles. But which rectangle will have the biggest area inside? Let's find out together!
Now let's make our first rectangle! We'll use our 20 centimeter rope to make a long and narrow rectangle. The length is 9 centimeters and width is 1 centimeter. Let's check: 9 plus 1 plus 9 plus 1 equals 20 centimeters - perfect! The area inside is 9 times 1, which equals 9 square centimeters. This rectangle is very long but not very wide.
Now let's try making different rectangles with our same rope! First, we made a 9 by 1 rectangle with area 9. Next, let's try 8 by 2 - that's 8 times 2 equals 16 square centimeters. Much bigger! Then 7 by 3 - that's 7 times 3 equals 21 square centimeters. Even bigger! Do you see the pattern? As the length and width get closer to each other, the area gets bigger!
And now for the amazing discovery! When we make the length and width exactly equal - both 5 centimeters - we get a square! Let's check: 5 plus 5 plus 5 plus 5 equals 20 centimeters. Perfect! And the area is 5 times 5, which equals 25 square centimeters. This is the biggest area we can get with our rope! The square wins!
What an amazing discovery we made today! When we have a fixed perimeter, the rectangle with the biggest area is actually a square! Remember: the closer the length and width are to each other, the bigger the area becomes. It's like having the same amount of fence to build a garden - making it square gives you the most space to plant flowers! This is a very special mathematical rule that even grown-ups find fascinating!