Answer:
length = 68 feet
width = 36 feet
Area of each half of the garden = 1224 square feet
Step-by-step explanation:
See attached figure at the bottom
Let the length of the garden be l and width be l-32
Since the garden is divided into two halves, the length would be split into two parts each of l/2
So,
AE = [tex]\frac{l}{2}[/tex]
EB = [tex]\frac{l}{2}[/tex]
AD = l-32
BC = l-32
DF= [tex]\frac{l}{2}[/tex]
FC = [tex]\frac{l}{2}[/tex]
EF = l-32
Total fence required = Sum of all sides + Middle side
244 = AE + EB + AD + BC + FC + DF + AD + EF
244 = [tex]\frac{l}{2}+\frac{l}{2}+l-32+l-32+\frac{l}{2}+\frac{l}{2}+l-32[/tex]
[tex]3l+2l-(32+32+32)=244 = 244[/tex]
[tex]5l-96=244[/tex]
Add 96 to both sides
[tex]5l-96+96=244+96[/tex]
Cancel out -96 and +96 from the left side
[tex]5l=340[/tex]
Divide both sides by 5
[tex]\frac{5l}{5}=\frac{340}{5}[/tex]
Cancel out 5 from the top and bottom of the left side
l = 68
So, length = 68 feet
width = l-32
=>width = 68-32
=> width = 36 feet
Thus, [tex]AE = \frac{l}{2} = \frac{68}{2} = 34 feet[/tex]
EF = l-32 = 68-32 = 36 feet
Area of each half of the garden = AE * EF
=>Area of each half of the garden = 34 * 36
=> Area of each half of the garden = 1224 square feet
