Respuesta :
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
The length of the rectangle is 116 ft. and the width of the rectangle is 58. Then the area of the garden will be 6728 square ft.
What is a rectangle?
It is a polygon that has four sides. The sum of the internal angle is 360 degrees. In a rectangle, opposite sides are parallel and equal and each angle is 90 degrees. And its diagonals are also equal and intersect at the mid-point.
Let the length of the rectangle be x and the width of the rectangle be y.
Then the perimeter of the rectangle will be
[tex]\rm P = x + 2y = 232\\\\y = 116 - \dfrac{x}{2}[/tex]...1
Then the area of the rectangle will be
[tex]\rm A = xy\\\\A = x (116 - \dfrac{x}{2})[/tex] ...2
Taking the derivative of the equation 2, then we have
[tex]\rm A' = 116 - x \\\\x \ \ = 116[/tex]
The from the equation 1, we have
[tex]\rm y = 116 - \dfrac{116}{2}\\\\y = 58[/tex]
Then the area of the rectangle will be
Area = 116 × 58
Area = 6728
More about the rectangle link is given below.
https://brainly.com/question/10046743
