Apolice officer seals off the scene of an accident using a roll of yellow tape that is 304 feet long. what dimensions should be used to seal off the maximum rectangular area around the collision? (enter your answers as a comma-separated list.)

The dimension are 76, 76 feet      

Explanation:

Given total length of the tape =  304 feet

Let x be one dimension of the rectangle

     y be the other dimension of the rectangle

Therefore we know, Area of the rectangle = x . y

                         Also Perimeter of the rectangle = 2 (x + y)

                                                                     304 = 2 (x + y)

                                                                      152 = x + y

                                                                       y = 152 - x --------(1)

Therefore substituting this in the area of the rectangle,

      Area = x . (152 - x)

               = 152x - x²

Therefore to find the maximum area covered, we need to differentiate the area.

Therefore, = 152x - x²

                  152x - x² = 0

                   152 - 2x  = 0

                     152 = 2x

                      x = 76

Substituting the value of 'x' in the equation (1), we get

          y = 152 - x

           y = 152 - 76

           y = 76

Therefore the dimensions the get maximum area is  x = 76 and y = 76.

Hence the answer is ---

The dimension are 76, 76 feet      

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