Question

Marquise has 200 meters of fencing to build a rectangular garden. The gardens area (in square meters) as a function of the gardens width w (in meters) is modeled by:

Answer 1

Answer: 2500 meters²

Step-by-step explanation:

Perimeter: 200 = 4w  

             ⇒    50 = w

Area = w²

        = (50)²

        = 2500

       

Answer 2

The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

What is the area of the rectangle?

The area of the rectangle is the product of the length and width of a given rectangle.

The area of the rectangle = length × Width

The perimeter of the rectangle = 2( length + Width)

                                             200 = 2( length + Width)

                                         100 - w = L

The area of the rectangle = length × Width

                                            = w(100 - w)

                                            = (-w)²+ 100w

So,  (-w)²+ 100w where, a = -1 and b = 100

w = -100/2(-1)

w = 50

The area of the rectangle = (-w)²+ 100w

                                            = (-50)²+ 100(50)

                                           = 2500

Thus, The width of 50 meters will produce the maximum garden area of the rectangle of 2500 square meters.

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