SOLUTION: a rectangular garden is fenced on three sides with a wall forming the fourth side. The total lenght of the fence is 80m. The area of the garden is 750m^2. Find the dimensions of th

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a rectangular garden is fenced on three sides with a wall forming the fourth side. The total lenght of the fence is 80m. The area of the garden is 750m^2. Find the dimensions of th      Log On


   

Question 957716: a rectangular garden is fenced on three sides with a wall forming the fourth side. The total lenght of the fence is 80m. The area of the garden is 750m^2. Find the dimensions of the garden.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
L=length (Parallel to wall); W=width (Perpendicular to wall); A=area=750m^2
L+2W=80m
L=80m-2W
A=L*W Substitute for L
750m%5E2=%2880m-2W%29%28W%29
750m%5E2=80W-2W%5E2 Subtract 750m^2 from each side.
0=-2W%5E2%2B80W-750m%5E2 Multiply each side by (-1/2)
0=W%5E2-40W%2B375m%5E2
0=%28W-25%29%28W-15%29
W-25=0 or W-15=0 ANSWER 1: The width is 15 meters.(or 25m)
L=80m-2W=80m-2(15m)=80m-30m=50m ANSWER 2: The length is 50 meters.(or 30m)
CHECK:
A=L%2AW
750m%5E2=%2850m%29%2815m%29 or 750m%5E2=%2830m%29%2825m%29
750m%5E2=750m%5E2 or 750m%5E2=750m%5E2