Question

A police 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.)

Answer 1

The dimension are 76, 76 feet

Step-by-step 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,
`(dA)/(dx)` = 152x - x²

`(d)/(dx)` 152x -
`(d)/(dx)` 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