Justin wants to use 376 ft of fencing to fence off the greatest possible rectangular area for a garden. What dimensions should he use? What will be the area of the garden?
A. 89 x 99; 8811 ft
B. 92 x 96; 8832 ft
C. 94 x 94; 8836 ft
D. 93 x 95; 8835 ft
thinking the answer is d, am i correct
Does D have the largest area?
no, it would be C.
Yes, C is right.
To find the dimensions that would result in the greatest possible rectangular area, you can follow these steps:
1. Let's assume the length of the garden is L and the width is W. Therefore, we have two sides of length L and two sides of length W.
2. The perimeter of the rectangle is given as 376 ft. The perimeter is the sum of all four sides: 2L + 2W = 376.
3. Rearrange the equation to solve for one variable in terms of the other. Let's solve for L by subtracting 2W from both sides: 2L = 376 - 2W, or L = 188 - W.
4. Now, we can substitute this equation for L into the formula for the area of a rectangle, which is A = L * W. So, A = (188 - W) * W.
5. Expand the equation: A = 188W - W^2.
6. To find the dimensions that maximize the area, we need to find the value of W that maximizes this quadratic equation. Since the equation is in the form -W^2 + 188W, it will have a maximum value (since the coefficient of W^2 is negative).
7. The x-coordinate of the maximum point of the quadratic equation can be found using the formula x = -b / (2a), where a is the coefficient of W^2 and b is the coefficient of W. In this case, a = -1 and b = 188.
8. Plug in the values for a and b: W = -188 / (2 * -1) = 94.
9. Now that we have the value of W, we can substitute it back into the equation L = 188 - W to find the corresponding value of L: L = 188 - 94 = 94.
10. Therefore, the dimensions of the garden that would result in the greatest possible area are 94 ft by 94 ft.
11. Finally, to calculate the area, we can substitute these values into the area formula: A = 94 * 94 = 8836 ft.
Therefore, option C is correct. The dimensions of the garden are 94 ft by 94 ft, and the area of the garden is 8836 ft.