A police officer seals off the scene of an accident using a roll of yellow tape that is 272 feet long. What dimensions should be

Question

morpeh [17]

3 years ago

14

A police officer seals off the scene of an accident using a roll of yellow tape that is 272 feet long. What dimensions should be

used to seal off the maximum rectangular area around the collision?

Mathematics

1 answer:

klasskru [66] · Answer 1 · 2022-01-16T12:17:57+03:00

Answer:

68 feet square

Step-by-step explanation:

The rectangle with the maximum area for a given perimeter is a square. The perimeter of a square is 4 times the side length, so the side length of the square area will be ...

(272 ft)/4 = 68 ft

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<em>More formally ...</em>

You can let x represent the length of one side. Then the length of the other side for the given perimeter will be 136 -x, and the area will be the product ...

area = x(136 -x)

The area function is a quadratic with zeros at x=0 and x=136. The vertex (maximum area) will be at the value of x that is on the line of symmetry between these points, at their midpoint: x = (0 +136)/2 = 68. This value of x makes the rectangle a square.