A rectangle field with area of 300 square meters and a perimeter of 80 meters. What are the length and width of the field?

Let L represent length, let W represent
Width.

Perimeter is equal to 2L+2W for any rectangle, or
P=2L+2W

Area is equal to L*W for any rectangle, or
A=L*W

Here, the perimeter is 80 meters and the area is 300m^2.  How
can we use this information to find out answers?  Let's think and figure it
out.

L*W=300m^2

2L+2W=80m
>>>>>>>>
2(L+W)=80>>>>>>> (L+W)=80/2
=40

L+W=40 then L=40-W  OR W=40-L  Choose one or the other to use in
the equation for area.

A=L*W>>> 300m^2 =
L*(40-L)

300m^2=40L-L^2
>>>>>>rewrite>>> L^2-40L+300=0
>>>now solve for L by factoring this equation to get (L-30)(L-10)=0
Therefore L=30 or L = 10.  It would make more sense that the length would be the longest
dimension so we will say that L=30.  Then W would have to be 10.  The rectangle is 30m long and
10m wide.  Just to be sure, let's multiply L*W to see if we get 300m^2, which we know is the area
of this rectangle.

Is 10*30 = 300?  Yes, it is.  Therefore
10m*30m=300m^2

Now lets check the Perimeter: 80 = 2L+2W OR 80 = 2*30
+ 2*10  >>>> 60+20=80  Is that correct?  I think it is.  Now you have
your solution.  The length of this rectangle is 30 meters and the width of it is 10 meters.  That
wasn't too difficult, was it?