77.3k views
5 votes
6. The area of a rectangular field is 2000 meters and its perimeter is 180 meters. Find the length

and width of the field.

1 Answer

3 votes

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))

User Jklaus
by
7.8k points

No related questions found