a certain type of fencing comes in rigid 10 foot long sections. Four uncut segments are to be used to fence in a garden on the side of a building. what value of x will make the garden as large as possible?
To find the value of x that will make the garden as large as possible, we need to determine the dimensions of the garden using the four 10-foot long sections of fencing.
Let's assume that the width of the garden is x feet. In this case, the length of the garden would be (10 - 2x) feet, because we have to subtract the width from each end to account for the corners.
To maximize the area of the garden, we calculate the product of the length and width, which is given by:
Area = length × width = (10 - 2x) × x
Expanding this equation, we get:
Area = 10x - 2x^2
To find the value of x that maximizes the area, we can take the derivative of the equation with respect to x and set it equal to zero. This will give us a critical point, which is where the maximum area occurs.
Differentiating the equation with respect to x, we get:
d(Area)/dx = 10 - 4x
Setting this derivative equal to zero:
10 - 4x = 0
Solving for x, we find:
4x = 10
x = 10/4
x = 2.5
Therefore, the value of x that will make the garden as large as possible is 2.5 feet.
No idea. What's x?
4 uncut lengths will for a square, the quadrilateral which has the largest area for a given perimeter.