Open Middle®
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
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.
20
the length is 4 yards the width is either 2 feet or 2 yards
so…4 yards and 2 feet or 6 yards
I said 6 because it said an area of 24 so I just divided.
I got four because 24 divided by 4 is 6
28 because you divide it And add 12 +2 +12+ 2
Hi, this is Zain Johar my answer is P 3+8+3+8= 22
I THINK IT IS 24 BECAUSE A RECTANGLE YOU CAN CUT IT IN HALF EACH IS 4
I think 6 because 6 times 4 equals 24
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.
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.
I got 13in and 4in.
i got a 5×24 but that is temporarily correct :/
i mean the real awnser
I say 6 because 24 divided by 4=6 and 6×4=24
I’m pretty sure its 6 cause 6 multiplied times 4 is 24.
8 Because 8×3=24 and 24 divided by 3 is 8
The perimeter is 6 plus 4 plus 6 plus 4 that equals 22. So the perimeter is 22
if you have an area of 24 square units it would be 12+12+2+2= 28 for the perimeter.
12+12+2+2=24
I’m picking 6×4 because it = 24
6×4 because it = 24
6 Times 4 because it = 24
I think the answer is 6×4 because 6×4 = 24
there are an infinite number of rectangles!
24 x 1
The greatest perimeter is 50 square units.
as i remember from my whiteboard, the greatest perimeter is 20.
I think it is 6 x 4 because it equals 24.
For those curious what the optimal solution would be:
Since we know that
A = a * b = 24
we can derive, that
a = 24/b
The perimeter u is therefore
u = 2 * a + 2 * b = 2 * 24/b + 2 * b = 48 / b + 2 * b
The derivative u'(b) = -48/b² + 2 is equal to 0 iff b = sqrt(6)/12.
It follows that a = 24/b = 48 * sqrt(6)
Meaning, the longest possible perimeter is that of a sqrt(6)/12 (≈0,2) by 48 * sqrt(6) (≈ 117,6) rectangle. It has a perimeter of
u(sqrt(6)/12) = 48/(sqrt(6)/12) + 2 * sqrt(6)/12 = 577/6 * sqrt(6) = 235,55926… ≈ 235,56 units
Correction:
The derivative u'(b) = -48/b² + 2 is equal to 0 iff b = +- 2*sqrt(6), but we can exclude the negative solution.
It follows that a = 24/b = 24/(2*sqrt(6)) = 12/sqrt(6) = 2 * sqrt(6)
Then u(b) = u(2 * sqrt(6)) = 8 * sqrt(6) ≈ 19.6
However, u(2 * sqrt) is not a maximum, but a local minimum. The function u doesn’t have a global maximum, as it tends to infinity for x -> 0+ and for x -> +infinity.
10 dimes