# Rectangles: Maximizing Perimeter

Directions: What is the greatest perimeter you can make with a rectangle that has an area of 24 square units?

### Hint

What are the possible dimensions of a rectangle that has an area of 24 square units?  How can we determine their perimeter?

### Answer

There are an infinite number of rectangles with an area of 24 square units.  Students may think that a 1 x 24 rectangle has the greatest perimeter, but a .5 x 48 rectangle has an even greater perimeter.  A .25 x 96 rectangle has an even greater perimeter.  So, there is no finite answer.

Source: Robert Kaplinsky

## Product Close to 1,000

Directions: Using the digits 1 to 9 at most one time each, place a digit …

### 31 comments

1. hey this is Brendyn Mahon and I did your area and perimeter problem and It was a little tricky but I got through It and I don’t really get It so I did It any way but I got the answer right.

2. the length is 4 yards the width is either 2 feet or 2 yards

3. so…4 yards and 2 feet or 6 yards

4. I said 6 because it said an area of 24 so I just divided.

5. I got four because 24 divided by 4 is 6

6. 28 because you divide it And add 12 +2 +12+ 2

7. Hi, this is Zain Johar my answer is P 3+8+3+8= 22

8. I THINK IT IS 24 BECAUSE A RECTANGLE YOU CAN CUT IT IN HALF EACH IS 4

9. I think 6 because 6 times 4 equals 24

10. Wow this was a little hard,but I think I got the right answer.I think the answer is a 1 by 24 rectangle because I think it has the strongest answer of all others.

11. There are an infinite number of rectangles with an area of 24 square units. Students may think that a 1 x 24 rectangle has the greatest perimeter, but a .5 x 48 rectangle has an even greater perimeter. A .25 x 96 rectangle has an even greater perimeter. So, there is no finite answer.

12. I got 13in and 4in.

13. i got a 5×24 but that is temporarily correct :/

14. i mean the real awnser

15. I say 6 because 24 divided by 4=6 and 6×4=24

16. I’m pretty sure its 6 cause 6 multiplied times 4 is 24.

17. 8 Because 8×3=24 and 24 divided by 3 is 8

18. The perimeter is 6 plus 4 plus 6 plus 4 that equals 22. So the perimeter is 22

19. Isabella Mendoza

if you have an area of 24 square units it would be 12+12+2+2= 28 for the perimeter.

20. I’m picking 6×4 because it = 24

21. 6×4 because it = 24

22. 6 Times 4 because it = 24

23. I think the answer is 6×4 because 6×4 = 24

24. there are an infinite number of rectangles!

25. The greatest perimeter is 50 square units.

26. as i remember from my whiteboard, the greatest perimeter is 20.

27. I think it is 6 x 4 because it equals 24.