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Answer:
option (A) 900 ft²
Step-by-step explanation:
Let the length be L and width of the area be 'B'
now,
Perimeter of the fence = 2 (L + B)
also,
2 (L + B) = 120 feet
or
L + B = 60 ft
or
L = 60 - B ft
Now,
The area of the fencing ground, A = LB
or
A = (60 - B)B
A = 60B - B²
now,
differentiating the area with respect to width B, we get
or
= 60 - 2B
for point of maxima or minima, put = 0
thus,
60 - 2B = 0
or
2B = 60
or
B = 30 ft
to check for maxima or minima
= - 2
since,
is negative, B = 30 ft is point of maxima
therefore,
L = 60 - B = 60 - 30 = 30 ft
Thus,
Maximum area of the fencing ground = 30 × 30 = 900 ft²
Hence,
The correct answer is option (A) 900 ft²