24 meter of fencing is used to fence a rectangular garden. let M represent the number of square meters in the area of the garden. what is the largest value that M could have?

Step-by-step explanation:

112 feet of fence is the length of the fencing.  The area of a rectangle is length times width.  The perimeter of a rectangle is the sum of twice the length and twice the width.

Let length = x

Let width = y

Use these variables to create equations.

2(x + y) = 112              eq1

x + y = 56                    eq1

Area = xy                       eq2

Substitute eq1 into eq2 to get a function area in terms of only x and y.

Area = x(56 - x)

Area = -x2 + 56x

The area represents a parabola that opens downward.  What you need to do is find the vertex of this parabola.

Find the x-coordinate of the vertex using this formula:

x = -b / (2a)

where:

a = -1

b = 56

Plug in these values into the formula.  Then evaluate the area at that x-coordinate.    That will be your maximum area.

i think this could be a possible answer (1 / 84) -1

good luck! : d