Answer:
11.1 by 28.9 meters
Explanation:
We can start by setting two variables: x for the width of the rectangle, and y for the length.
the perimeter is 80 meters, and use our formula for perimeter (p = 2l + 2w, where l is length and w is width), we can construct an equation:
2x + 2y = 80
We can divide by 2 on both sides:
X + y = 40
We can isolate x:
X = 40 -y
we also know that the area is 320. Using our formula for area (a = lw, where l is length and w is width), we can construct another equation:
xy = 320
We can substitute x from our past equation in here
(40-y)y = 320
Multiply in distributor
40y - y^2 = 320
Add:
Y^2 -40y +320 = 0
We can find our roots using the quadratic formula, and they are:
20 + 4√5, and 20 - 4√5
Rounded to the nearest 10th, we get:
28.9 and 11.1
we can plug this into our first equation where x = 40-y
X = 40 - 28.9 = 11.1
X = 40 - 11.1 = 28.9
Since we have the same two values for each variable, that gives us the dimensions: 11.1 by 28.9 meters