Mathematics, 30.07.2019 11:30, deadlydazy13

You have a 64 foot of fencing. what are the dimensions of the rectangle of the greatest area you could enclose?

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In a rectangle, opposite sides are congruent.
Let one side have length x.
The opposite side also has length x.
The lengths of these two sides add to 2x.
The lengths of all 4 sides add to 64, so the lengths of the other 2 sides
add up to 64 - 2x. Each side measures 32 - x.

The rectangle has sides of length x and 32 - x.

The area of the rectangle is

A = LW

A = x(32 - x)

A = 32x - x^2

y = 32x - x^2 is a parabola that opens downward.
The maximum value of the parabola is the vertex on top.

32x - x^2 = 0

(32 - x)x = 0

32 - x = 0 or x = 0

x = 32 or x = 0

Since the parabola is symmetric with respect to the vertical axis, the vertex has x-coordinate 16.

At x = 16, you get maximum area.

Two opposite sides measure 16 ft each.
32 - x = 32 - 16 = 16
The other two opposite sides also measure 16 ft.

Since all sides turned out to have length 16 ft, the rectangle is a square.

The maximum area is enclosed by a square with side 16 ft.

answered: Guest

Try a or d, hope that

answered: Guest

let's cover over the formula of the vertex:

y = a(x – h)^2 + k

in this formula, (h,k) are the vertex, always remember that the positive or negative value of the vertex is based on the sign it has.

for example, if the vertex is -3,-6 then both the x and y value would have the positive sign attached to it and if it were a positive x and y value, then a negative sign would be attached to it.

with that being said, for our problem the x value is a positive one so we are looking for a number with a negative sign next to it, in this case the first and second choice.

however, for the first answer choice it isn't quite part of the formula so we know that the answer choice correctly displays the x value.

to confirm, we can see if the -1 fits correctly with the second answer choice, and as mentioned above a negative number will have a positive sign attached to it. so, for our problem we can see that -1 has been changed to +1, so we can confirm that the second answer choice is correct.

hence, our final answer is y=(x - 1)^2 + 1

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You have a 64 foot of fencing. what are the dimensions of the rectangle of the greatest area you cou...