Answer:
Width which gives maximum area = 13 feet
Maximum Area = 169 [tex]feet^2[/tex]
Step-by-step explanation:
Given: 52 feet of fencing means Perimeter of rectangular dog pen.
If Total length of the boundary of rectangle (.i.e., Perimeter) is fixed then the rectangle with equal sides has the maximum area.
Width = x (given)
∴ for maximum area let length = x
Perimeter of rectangle = 52 feet
2 × (Length + Width) = 52
2 × ( x + x ) = 52
2 × ( 2x ) = 52
4x = 52
x = [tex]\frac{52}{4}[/tex]
x = 13 feet.
Maximum Area = Length × Width
= 13 × 13
= 169 [tex]feet^2[/tex]
Width which gives maximum area = 13 feet
Maximum Area = 169 [tex]feet^2[/tex]
