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

check the picture below.

well, the angle at the vertex d is clearly not a right-angle, let's check for the one at the vertex f which does look like,   however if it's indeed, that means ef is perpendicular to df, in which case their slopes will be negative reciprocal of each other.

so the negative reciprocal of the slope of ef is 1, however the slope of df is not 1, is 1/2, so nope, they're not perpendicular lines.

30

step-by-step explanation:

idk

i hope i