mr.king, the owner of good morning groceries, wants to make a fence aea to put his carts in at night.he has 68 feet of fencing.what is the largest rectangular area he can fence? ( use only whole numbers)
Largest rectangle is a square
P = 2w + 2L
68 = 2w + 2L
34 = w + L
34/2 = 17
34 = 17 + 17
Dimension = 17 x 17
68/4 = ?
To find the largest rectangular area that Mr. King can fence with 68 feet of fencing, we need to consider the dimensions of the rectangle. Let's assume the width of the rectangle is w, and the length is l.
Now, we know that the perimeter of a rectangle is given by the formula P = 2(w + l). In this case, the perimeter is 68 feet. So, we can rewrite the formula as 68 = 2(w + l).
We want to find the largest area, which is given by the formula A = w * l. To simplify the problem, we can express one of the variables in terms of the other. Let's solve the perimeter equation for l.
68 = 2(w + l)
Divide both sides by 2 to isolate (w + l):
34 = w + l
Now, we can subtract w from both sides to express l in terms of w:
l = 34 - w
Substitute this value of l into the area equation:
A = w * (34 - w)
Simplify:
A = 34w - w^2
Now, we have the area in terms of w. To find the value of w that maximizes the area, we can take the derivative of A with respect to w and set it equal to zero.
dA/dw = 34 - 2w
Set it equal to zero and solve for w:
34 - 2w = 0
2w = 34
w = 17
Now that we have the width, we can substitute it back into the equation to find the length:
l = 34 - w
l = 34 - 17
l = 17
Therefore, the dimensions of the rectangle that yield the largest area with 68 feet of fencing are 17 feet by 17 feet. The largest rectangular area Mr. King can fence is 17 * 17 = 289 square feet.