Answer:
Step-by-step explanation:
From the given information:
Since three sides of the garden need to be enclosed because the fourth side is a building.
The area is xy and the perimeter will be x + 2y
Calculating the perimeter in terms of x; we have:
P = x+2y = 232 ----- (21)
y = (232 - x) / 2
y = 116 - (x/2)
Now; to calculate the area since the value of y in terms of x is known.
A = xy
A = x[116 - (x/2)]
A=116x - (x^2/2) ----- (2)
Taking the derivative of eqaution (2); we have:
A' = 116 - x
Relating it as it is equal to zero, thereby solving for x
; we have:
116 - x = 0
x = 116
From equation (1)
P = 116 +2y = 232
2y = 232 -116
2y = 116
y = 116/2
y = 58
Thus; the area A = xy can be calculated as:
A=xy
A=116(58)
A= 6728
