SOLUTION: Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the tape, he must divide the area into four identical rectangular sections, side by side. What d

Question 1172917: Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the tape, he must divide the area
into four identical rectangular sections, side by side. What dimensions of the crime scene will maximize the area?
What is the maximum area that can be enclosed?
pls i need the help now its really difficult for me thank u
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
draw this.
The length is x
the width is y
The area of the whole rectangle is xy. The perimeter is 2x+2y=300 or x+y=150, so y=150-x
the area of each of the rectangles is x(1/4)y, and this is x(37.5)-x^2.
This quadratic is maximized when x=-b/2a=-37.5/-2 or x=18.75 feet.
That means that 4 of them are 75 feet and the area of the whole rectangle is 75 ft*75 ft=5625 ft^2. It is a square.

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