Answer: Length = 90 meters
Width = 20 meters
Step-by-step explanation: Step 1: The formula for the area of a rectangle is A = length x width, so we can solve for the length of the field:
A = 2000
length x width = 2000
length = 2000 / width
Step 2: The formula for the perimeter of a rectangle is P = 2(length + width), so we can solve for the width of the field:
P = 180
2(length + width) = 180
2length + 2width = 180
2width = 180 - 2length
width = (180 - 2length) / 2
Step 3: Substitute the equation for width into the equation for length to solve for length:
A = 2000
length x (180 - 2length) / 2 = 2000
2length2 - 180length + 2000 = 0
length2 - 90length + 1000 = 0
(length - 90)(length - 10) = 0
length = 90
Step 4: Substitute the value of length into the equation for width to solve for width:
width = (180 - 2length) / 2
width = (180 - 2(90))