Marcus has 68 ft of fencing. He wants to build a rectangular pen with the largest possible area. What should the dimensions of the rectangle be?
a. 19 by 21
b. 21 by 13
c. 17 by 17
d. 19 by 15
I got a. Is this right?
hello, is there any math expets that are online now?
17 by 17
To find the dimensions of the rectangle that would create the largest possible area with 68 ft of fencing, we can use the concept of calculus. The perimeter of a rectangle is given by the formula P = 2l + 2w, where l represents the length and w represents the width. In this case, we have a total of 68 ft of fencing, so 2l + 2w = 68.
To find the dimensions of the rectangle that maximize the area, we need to solve for one variable in terms of the other. Solving the perimeter equation for l, we get l = (68 - 2w) / 2 = 34 - w.
The area of a rectangle is given by the formula A = lw. Substituting the expression for l, we have A = w(34 - w) = 34w - w^2.
To find the maximum area, we need to find the critical points of this function. Taking the derivative of A with respect to w, we get dA/dw = 34 - 2w.
Setting dA/dw = 0 to find the critical points, we have 34 - 2w = 0. Solving for w, we get w = 34/2 = 17. So, the width of the rectangle that maximizes the area is 17 ft.
Substituting this value back into the equation for l, we have l = 34 - w = 34 - 17 = 17 ft. Therefore, the dimensions of the rectangle that would create the largest possible area with 68 ft of fencing are 17 ft by 17 ft.
So, the correct answer is c. 17 by 17.