One Fence, Three Gardens
A gardener buys 12 feet of fence. She wants to fence in a rectangle of soil for her tomato plants. The question is, what shape of rectangle gives the plants the most room?
First, two words. The perimeter is the distance around the outside of a shape. For her garden, the perimeter is the 12 feet of fence. The area is the space inside the shape. It is measured in square feet, and you find it by multiplying the length by the width.
She can make three different rectangles with whole-number sides. One is 1 foot wide and 5 feet long. Add 1, 5, 1, and 5 to check the fence, and you get 12. Its area is 1 times 5, which is 5 square feet.
Another is 2 feet wide and 4 feet long. Again 2 plus 4 plus 2 plus 4 makes 12 feet of fence. Its area is 2 times 4, or 8 square feet.
The third is 3 feet wide and 3 feet long, a square. The fence is still 12 feet. Its area is 3 times 3, which is 9 square feet.
The same fence made three gardens, and the gardens were not the same size. The square held the most. The long, skinny garden held the least. A shape that is closer to a square usually fits more room inside the same fence.