the perimeter of a rectangular campsite is 64m and its area is 207m^2. find the length and breadth of the campsite
Accepted Solution
A:
Answer:The length is [tex]23\ m[/tex] and the breadth is [tex]9\ m[/tex]Step-by-step explanation:Letx ----> the length of a rectangular campsite y ----> the breadth of a rectangular campsite we know thatThe 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 AThe area of a rectangle is equal to[tex]A=xy[/tex][tex]A=207\ m^{2}[/tex]so[tex]207=xy[/tex] -----> equation Bsubstitute 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 graphingThe solution is [tex]x=23\ m[/tex] ( I assume that the length is greater than the breadth)see the attached figureFind the value of y[tex]y=32-23=9\ m[/tex]thereforeThe length is [tex]23\ m[/tex] and the breadth is [tex]9\ m[/tex]