Someone help explain?
Justin wants to use 188 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?
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A. 89 ´ 99 ; 8811 ft
B. 92 ´ 96 ; 8832 ft
C. 94 ´ 94 ; 8836 ft
D. 93 ´ 95 ; 8835 ft
none of the choices has a perimeter of 188 ft. All have a perimeter of 376 ft.
A square has maximum area for a given perimeter, so the garden should be 47 by 47, with area = 2209.
Assuming one of the given choices, you'd want a square, so go with 94x94. Heck, the table shows it has the largest area.
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
To find the dimensions of the rectangular area that will enclose the greatest possible garden, we need to use the given 188 ft of fencing efficiently.
Let's assume the length of the rectangular garden is x ft. In that case, the width of the garden would be (188 - 2x) ft because we have to subtract the length of the two sides from the total fencing.
To find the maximum area, we need to find the dimensions that will result in the maximum product of the length and width. Therefore, we need to find the maximum value of the product A = x * (188 - 2x).
To find the maximum value, we can use derivatives. By differentiating A with respect to x and setting it equal to zero, we can find the critical points. By analyzing the second derivative, we can determine whether these critical points correspond to the maximum or minimum.
Differentiating A with respect to x:
A' = 188 - 4x
Setting A' equal to zero:
188 - 4x = 0
4x = 188
x = 188/4
x = 47
To determine whether this is a maximum or minimum, we differentiate A' with respect to x again:
A'' = -4
Since A'' = -4 < 0, it means that the critical point x = 47 corresponds to the maximum area.
Therefore, the length of the rectangular garden should be 47 ft, and the width will be (188 - 2 * 47) = 94 ft.
The correct answer is option C: 94' x 94' with an area of 8836 ft².