A rectangular playground is to be fenced off and divided in two by another fence parallel to one side of the playground. Six hundred feet of fencing is used. Find the dimensions of the playground that maximize the total enclosed area. What is the maximum area?

the smallest dimension = 100 ft

the largest dimension = 150 ft

Maximum Area = 15000 ft²

Step-by-step explanation:

let x represent length of one side and L represent length of adjacent side

so from the question

3x + 2L = 600

2L = 600 - 3x

L = (600 - 3x)/2

L = (600/2) - (3x/2)

L  = 300 - (3x/2)

now Area of rectangle = L × x

Area = (300 - (3x/2)) × x

Area = 300x - 3x²/2

now we differentiate with respect to x  and equate to 0 in other to find critical point

dA/dx ⇒ 300x/x - 3x²/x = 0

300 - 3x = 0

3x = 300

x = 300/3

x = 100

so we input value of x into our previous equation

Area = 300x - 3x²/2

= 300(100) - (3(100)²)/2

= 30000 - 15000

Area = 15000

also we input value of x in L = 300 - (3x/2)

L  = 300 - (3(100))/2)

L = 300 - 150

L = 150

Therefore

the smallest dimension = 100 ft

the largest dimension = 150 ft

Maximum Area = 15000 ft²

alright well the answers to your question is

2xy/9 hope this have a nice day : )

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.