A police officer seals off the scene of an accident using a roll of yellow tape that is 396 feet long.

Question

What dimensions should be used to seal off the maximum rectangular area around the collision? Also find maximum area.

Answer 1

P=2l+2w

396=2l+2w

divide both sides by 2

198=l+w

198-w=l

A=lw

A=(198-w)(w)

A=198w-w^2

this is a parabola that opens downward and has vertex (h,k) where h="the maximizing width" and k=the area

use -b/2a

-198/-2=99 feet

you want a square 99 feet by 99 feet

A=99*99=9801 square feet

Note: the maximum area will always be a square; therefore all you had to do was 396/4=99 feet

however, depending on what level of math you are in, you probably need the algebra work