Respuesta :
Answer:
The dimension are 76, 76 feet   Â
Explanation:
Given total length of the tape = Â 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, [tex]\frac{dA}{dx}[/tex] = 152x - x²
         [tex]\frac{d}{dx}[/tex] 152x - [tex]\frac{d}{dx}[/tex] 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   Â
