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Find the dimensions of a rectangular flower garden with a maximum area that can be enclosed by a 100 m fence. What is the maximum area?

Let L and W be the dimensions:

Given: Area = at maximum , P = 100 m

We know that P = 2(L+W) , thus

• P = 2(L+W)
• 100 = 2(L+W)
• 100÷2 = L+W
• 50 = L+W

so ,

• L = 50-W

Then Area = LW , therefore

• A = LW
• A = (50-W)(W)
• A = 50W-W²

Get the derivative using power rule:

Then equate the derivative to 0

• 0 = 50-2W
• -50 = -2W
• -50/-2 =W
• 25 = W

Now that we get the value of W , we will find the value of L

• L = 50-W
• L = 50-25
• L = 25

Henceforth , the dimensions are 25 meters by 25 meters

Lastly , we will solve for the maximum area

• A = LW
• A = (25)(25)
• A = 625m²

Therefore , the maximum area measures 625m²

• The dimensions are 25 meters by 25 meters
• The maximum area is 625m²