Idea 17of 22Builds onSame area, different perimeters
Close to a square needs the least fence
Which rectangle of one area has the shortest perimeter?
Today you'll discover
- the two extremes
- which shape saves fence
- how to use it on a pen
Think firstFour rectangles, each 24 m²
Which of the four needs the least fence?
Decide first, then press Next. Compare the shapes, from long and thin to nearly square.
Four rectangles of 24 m² drawn to one scale: 24 by 1, 12 by 2, 8 by 3 and 6 by 4. Their perimeters appear: 50 m, 28 m, 22 m and 20 m. The 6 by 4 is ringed in green as least fence, the 24 by 1 in orange as most fence. The last step shows four dog pens of 36 m².
See the whole ideathe big idea and the key word, in one place
The big idea
For one area, the rectangle closest to a square has the least perimeter; long and thin, the most.
Squarer, shorter
The same 24 m², with the fence shrinking as the shape gets squarer.
- 24 by 150 m
- 12 by 228 m
- 8 by 322 m
- 6 by 420 m
Where it goes nextFarmers and builders use this to save fencing: the squarer the pen, the less fence to buy.
Key word
- square
- a rectangle with four equal sides
Ready to use it?
- Choose the rectangle with the least perimeter for a given area.