SOLUTION: Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the tape, he must divide the area into four identical rectangular sections, side by side. What d

Question 1172937: Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the tape, he must divide the area
into four identical rectangular sections, side by side. What dimensions of the crime scene will maximize the area?
What is the maximum area that can be enclosed?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the tape, he must divide the area into four identical rectangular sections, side by side.
What dimensions of the crime scene will maximize the area?
To divide into 4 areas, it requires 5 dividing sides and 2 lengths
2L + 5w = 300
simplify, divide by 2
L + 2.5w = 150
L = 150 - 2.5w
Area = L*w
replace L with (150-2.5w)
A = w(150-2.5w)
A = 150w - 2.5w^2
A quadratic equation where b=150 and a=-2.5
The max area occurs on the axis of symmetry, find that using x=-b/(2a)
w =
w = 30 meters is the width
Find the length
L = 150 - 2.5(30)
L = 75 meters is the length
:
What is the maximum area that can be enclosed?
75 * 30 = 2250 sq meters
RELATED QUESTIONS
Officer Mark has 300 m of yellow tape to seal off the area of a crime scene. Using the... (answered by Boreal)

1.A police officer is investigating a crime which occurred in a rectangular field next to (answered by ankor@dixie-net.com)

Use completing the square to write the following equations in vertex form. State the... (answered by josgarithmetic)

Police seals off the scene of the accident ( in a rectangle) with tape 300ft long. What... (answered by solver91311)

Phillip used four pieces of masking tape, each 6 inches long, to put up each of his... (answered by mananth)

joe wants to paint a rectangular region of a wall with one layer of paint. he has 40 ft... (answered by josmiceli)

Phillip used four pieces of masking tape, each 6 inches long, to put up each of his... (answered by checkley79)

You want to mark off a square region in your yard for a patio. You use a tape measure to (answered by richwmiller)

Hi a tent has the shape of a triangular prism with dimensions as follows:base 1.6m side... (answered by KMST)