Answer:
18 meters by 14 meters
Step-by-step explanation:
Area of rectangle is base times height (AKA length times width or however you wish to call the dimensions).
This question is a system of equations question. We can make two equations. We know that every rectangle must have 2 "lengths" and 2 "widths" (4 sides in a rectangle). Since Maria only has 64 meters of fencing, we get the equation:
2L+2W = 64
Now we know the area enclosed must be 252 so we have:
L* W = 252
Rewriting the second equation we get: [tex]W=\frac{252}{L}[/tex]
Plug this into first equation to get: [tex]2L+2\left(\frac{252}{L}\right)=64[/tex]
[tex]2L+\frac{504}{L}=64[/tex]
[tex]2L^2+504=64L[/tex] (multiply everything by L)
Solving the quadratic tells us L can be 18 or 14. Let's consider if L is 18 first by plugging 18 back into the second equation to get 18 * W = 252 which gives us W = 14. If we do the same for when L = 14, we get that W = 18.
Now you might wonder why we have 2 possible combinations, that's because in reality, it doesn't matter which one we label as length (L) or width (W).
