A lifeguard marks off a rectangular swimming area at a beach480 m of rope. What is the greatest possible area she can enclose?

Answer 1

Either #28,800# or #14,400# square meters depending upon the interpretation of the description.

Option 1: One side of the rectangle is formed by the beach (no rope needed)

If #L# represents the length of the side paralleling the beach and #W# represents the with of the remaining two sides perpendicular to the beach then #color(white)("XXX")L=480-2Wcolor(white)("xxxxx")#(all measurements in meters) and the area would be #color(white)("XXX")A_(L,W)= LxxW# or #color(white)("XXX")A(W)=480W-2W^2#
The maximum value for #A(W)# would be achieved when the derivative #A'(W)=0#
#color(white)("XXX")A'(W)=480-4W=0#
#color(white)("XXX")rArr W=120#
and, since #L=480-2W# #color(white)("XXX")rArr L=240#
Giving a total possible area of #color(white)("XXX")LxxW= 240xx120=28,800# (square meters)
Possibility 2: All 4 sides require rope In this case the maximum area is formed by a square with sides of length #480/4=120# (meters) and a (maximum) area of #120xx120=14400# square meters
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Answer 2

To maximize the area, the lifeguard should form a square with side length of 120 meters. The greatest possible area is 14,400 square meters.

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Answer 3

To maximize the area, the lifeguard should form a square swimming area with the given rope length.

The formula for the area of a square is side length squared.

So, if 480 meters of rope is used to form a square, each side length would be 480/4 = 120 meters.

Therefore, the greatest possible area she can enclose is 120 meters * 120 meters = 14400 square meters.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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