SOLUTION: A farmer plans to enclose a rectangular field, whose length is 16 meters more than its width, with 140 meters of chain-link fencing. What are the dimensions of the field?

Question 565545: A farmer plans to enclose a rectangular field, whose length is 16 meters more than its width, with 140 meters of chain-link fencing. What are the dimensions of the field?
Answer by Leaf W.(135) (Show Source): You can put this solution on YOUR website!
The 140 meters of chain-link fencing represents the perimeter of the rectangular field. Since perimeter is the sum of the lengths of a figure's sides, the perimeter of the field is width + length + length + width, or 2(width) + 2(length). Now let us find some variable expressions for the length and width:
width: x
length: x + 16 (16 meters more than the width)
Now plug these values for perimeter, width, and length into the equation:
perimeter = 2(width) + 2(length)
140 = 2x + 2(x + 16)
Distribute the 2: 140 = 2x + 2x + 32
Add like terms: 140 = 4x + 32
Subtract 32 from both sides: 108 = 4x
Divide both sides by 4: 27 = x
=> The width of the field is 27 meters.
To find the length, put this value in for x in the expression for length: x + 16 = 27 + 16 = 43
=> The length of the field is 43 meters.
***THEREFORE, THE LENGTH OF THE FIELD IS 43 METERS AND THE WIDTH IS 27 METERS.***
Hope I helped! =)
RELATED QUESTIONS
Farmer Dan has 170 meters of fence with which to enclose a field. The length of the field (answered by josmiceli)

Farmer Dan has 167 meters of fence with which to enclose a field. The length of the field (answered by checkley79)

a farmer encloses a rectanglar field whose width is 40 meters with 210 meters of chain... (answered by jojo14344)

the length of a rectangular field is 7 meters more than twice it width. the perimeter is... (answered by checkley77)

A rectangular field whose length is 10 meters longer than its width is to be enclosed... (answered by Cromlix)

A Rectangular field whose length is 10 meters longer than its width is to be enclosed... (answered by Earlsdon)

A rectangular field whose length is 10 meters longer than its width is to be enclosed... (answered by jorel1380)

A rectangular swimming pool has a perimeter of 140 meters and a length that is 15 meters... (answered by ewatrrr)

Farmer Dan has 2736 feet of fence with which to enclose a field. The length of the field... (answered by macston)