What is the smallest perimeter you can make if the area of a rectangle is 24 units^2?
What is the largest perimeter you can make if the area of a rectangle is 24 units^2?
What is the largest perimeter for a rectangle with an area of 100 units^2?

Smallest perimeter = 19.6 units

Largest perimeter for area of 24 u2 = 50 units (assuming smallest side = 1 unit)

Largest perimeter for area of 100 u2 = 202 units (assuming smallest side = 1 unit)

Step-by-step explanation:

The area of a rectangle is:

Area = length * width

If the area is 24 u2, we have that:

length * width = 24 -> length = 24/width

Then the perimeter is:

P = 2*length + 2*width = 48/width + 2*width

To find the smallest perimeter, we can take the derivative and make it equal to zero to find the width that gives the smallest perimeter:

dP/dwidth = -48/width^2 + 2 = 0

width^2 = 48/2 = 24

width = 4.9

so the length is 24/width = 24/4.9 = 4.9

and the perimeter is 2*4.9 + 2*4.9 = 19.6 units

To find the largest perimeter, we need to assume the smallest value that a side can have. Assuming that this value is 1 unit, we have that:

Area = length * 1 = 24

length = 24 units

Perimeter = 2*24 + 2*1 = 50 units

If the area is 100 u2, the largest area, again assuming smallest value for side equal 1 unit, is:

Area = length * 1 = 100

length = 100 units

Perimeter = 2*100 + 2*1 = 202 units

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