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

x =±sqrt(1/3)

step-by-step explanation:

x+4/6x=1/x

multiply each side by 6x to get rid of the fractions

6x*(x+4/6x)=1/x*6x

distribute

6x^2 +4 = 6

subtract 4 from each side

6x^2 +4-4 = 6-4

6x^2 =2

divide by 6

6x^2/6 = 2/6

x^2 = 1/3

take the square root of each side

sqrt(x^2) = ±sqrt(1/3)

x =±sqrt(1/3)

a.

step-by-step explanation:

step 1 distribute 2 to every term in the parentheses

step 2 add 10 on both sides of the equal sign