A police officer seals off the scene of an accident using a roll of yellow tape that is 248 feet long. What dimensions should be used to seal off the maximum re

Question

A police officer seals off the scene of an accident using a roll of yellow tape that is 248 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.)
               ft

 

What is the maximum area?

       ft^2

Answer 1

Kassandra:

 

I get the same answer of 62 feet squared = 3,844 sq. ft.

 

Simply divide the number of feet in the roll by 4, and that will end up with the largest 'rectangle' possible. 

 

Larry

Answer 2

Assume the dimensions of the rectangle are x and y

 

Then      Area = xy  (to be maximized)

&           2x + 2y = 248    (constraint)

 

From the constraint   y = 124 - x

 

Substitute in the expression for Area = xy = x(124-x)

 

differentiate area     dArea/dx = 124 - 2x  =0  =>  x = 62

Thus x= 62 & y = 62 maximizes the area.