Randy is building a fence at the side of his warehouse. He has 120 m of fencing and plans to use the side of the warehouse as one side of the rectangular fenced area. What are the dimensions of the
maximum area Randy can enclose?

please please answer this quick.

60 meters

Explanation:

"It will probably help to have a diagram to look at:

Since we're told that the fenced area is to be a rectangle, draw a rectangle.

Since one side is to be the barn, choose a side of the rectangle to be a the barn. (It doesn't matter which side you choose.)

Label the two sides of the rectangle that are connected to the barn as "x". (Since this is a rectangle these opposite sides should be the same.)

The hardest part is the side opposite the barn. We know that we have 120 meters of fence to use. It hope it makes sense that to get the maximum area we should use all the fencing. So the lengths of the three "non-barn" sides will be 120. So how do we express the length of the side opposite the barn? Well if we know what "x" was it would be easy. For example if x = 35 then the side opposite the barn would be 120 - 35 - 35 = 50. We now use this same logic even though we don't know what "x" is yet. The side opposite the barn will be

120 - x - x

which simplifies to:

120 - 2x

We can now find a solution. The area of any rectangle is length times width (or base times height). So for our rectangle the area will be: A = x (120 - 2x)

This is a quadratic equation so I am going to rewrite it in ax^2+bx+c: A=-2x^2 + 120x

We should recognize that the graph of a quadratic equation will be a parabola. And since the squared term is x^2 this parabola will open upward or downward. And since the "a" is negative (-2 to be specific), this parabola will open downward. If we picture a downward-opening parabola in our minds we should be able to understand that the vertex of the parabola will be the highest point of the graph. So the x-coordinate of the vertex will give the the maximum value for A, the area.

So we just need to figure out the x-coordinate of the vertex. This can be done by completing the square or by just knowing that the x-coordinate of the vertex would be '-b/2 + a.'

Our "b" is 120 and our "a" is -2 so the x-coordinate of the will be: -(120/2*(-2)) = 30

This is the x that gives us the maximum area. (If you're curious as to exactly what number this maximum area is, just substitute 30 for x into A=-2x^2+120x)

So we can label the two sides of "x" as 30's. And since the side opposite the barn is 120 - 2x, it will be 120 - 2(30) = 120 - 60 = 60 meters."

-jsmallt9

if this is really you s much. i only have 3 points left and i have 2 questions to ask

idk this answer sorry cant on this one.

step-by-step explanation: