Find the dimensions of a rectangle with perimeter 84 m whose area is as large as possible. (if both values are the same number, enter it into both blanks.)

All the sides of the rectangle are 21 m length.

Step-by-step explanation:

The problem is:

Maximize: Area = a*b (eq. 1)

subject to: 2*a + 2*b = 84 m (eq. 2)

where a and b are the length of the sides of the rectangle.

Isolating a for eq. 2:

a = 84/2  - 2/2*b = 42 - b (eq. 3)

Replacing in eq. 1:

Area = (42 - b)*b = 42b - b^2

In the maximum the derivative is equal to zero. Then:

d Area/d b = 42 - 2*b = 0

42 = 2*b

b = 21 m

Replacing in eq. 3:

a = 42 - b = 42 - 21 = 21 m

step-by-step explanation:

we are given

since, we have to isolate x on anyone side

so, we can move all x terms on one side

subtract both sides by 2x

add both sides by 9

divide both sides by 4

we get

10 - 75

step-by-step explanation:

there's nothing attached so it's most likely anything in that range.