Police officer Question

Question

A police officer is investigating a crime which occurred in a rectangular field next to a building. He wants to seal the three sides of the area around the scene with 300 m of yellow police tape. What is the maximum area that he can enclose, and what are the dimensions of this area?

Please answer in full details

Answer 1

You have 300m of tape to cover 3 sides of a rectangular area.

Perimeter = 300 = 2W + 1L (the wall is the 4th side).

Area = LW. L = 300 - 2W Substitute: Area = (300 - 2W)W = 300W - 2W²

Re-write as -2W² + 300W

The x value of the parabola's vertex (maximum) is at -b/2a or -(300)/2(-2) = 75m

So the sides are 75m each and the long dimension is 300 - 75 - 75 = 150m.

You could also take the 1st derivative and set = 0 (slope is = 0 at the max)

-4W + 300 = 0 → -4W = -300 W = 75m, etc.

Answer 2