Question

An angry student murdered Tommy the Turtle near the northern fence of the park. Using yellow tape,Ranger Dave is marking off a rectangular area around Tommy’s body.Since Tommy was murdered near the fence, Ranger Dave only needs tape for three sides.What is the least amount of tape Ranger Dave needs to use, if the Crime Scene Investigators need 450square feet to work?Remember to justify that you have found a minimum, and include units in your answer. Partial credit willbe given for sketching a picture, labeling and describing variables, etc.

Answer 1

Answer:

60ft

Step-by-step explanation:

Let's x, y be the width and length of the surrounding rectangle. Since the area is 450 sq feet, this means xy = 450 or y = 450/x

The perimeter of this rectangle is (since there are 3 sides only)

f(x,y) = 2x + y

This is something we need to minimize. We can start by substituting y = 450/x

f(x) = 2x + 450/x

Let's take the first derivative of this function and set it to 0

$f'(x) = 2 - \frac{450}{x^2} = 0$

$2 = \frac{450}{x^2}$

$x^2 = 450 / 2 = 225$

$x = \sqrt{225} = 15ft$

y = 450 / 15 = 30ft

so the minimum perimeter that needs taping over is

f(x,y) = 2x + y = 2*15 + 30 = 60ft