Answer:
The dimensions are 68 meters by 42 meters.
Step-by-step explanation:
Let the length be x
Let the width be y
Perimeter = 220 meter
So, [tex]2x+2y=220[/tex]
or [tex]x+y=110[/tex] or [tex]x=110-y[/tex] ...........(1)
Area = 2856 square meter
So, [tex]xy=2856[/tex] ............(2)
Substituting the value of x from (1) in (2)
[tex](110-y)y=2856[/tex]
=> [tex]110y-y^{2}=2856[/tex]
=> [tex]y^{2}-110y+2856=0[/tex]
Solving this equation, we get roots as y = 68 and y = 42
So, if we put y = 68, we get x = 42
If we put y = 42, we get x = 68
As length is longer than width, we will take length = 68 meters and width = 42 meters.
Hence, the dimensions are 68 meters by 42 meters.
