Answer:
The length is [tex]23\ m[/tex] and the breadth is [tex]9\ m[/tex]
Step-by-step explanation:
Let
x ----> the length of a rectangular campsite
y ----> the breadth of a rectangular campsite
we know that
The perimeter of a rectangle is equal to
[tex]P=2(x+y)[/tex]
[tex]P=64\ m[/tex]
so
[tex]64=2(x+y)[/tex]
[tex]32=(x+y)[/tex]
[tex]y=32-x[/tex] ------> equation A
The area of a rectangle is equal to
[tex]A=xy[/tex]
[tex]A=207\ m^{2}[/tex]
so
[tex]207=xy[/tex] -----> equation B
substitute equation A in equation B
[tex]207=x(32-x)\\\\207=32x-x^{2}\\\\x^{2}-32x+207=0[/tex]
Solve the quadratic equation by graphing
The solution is [tex]x=23\ m[/tex] ( I assume that the length is greater than the breadth)
see the attached figure
Find the value of y
[tex]y=32-23=9\ m[/tex]
therefore
The length is [tex]23\ m[/tex] and the breadth is [tex]9\ m[/tex]
