|
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! =)
|
|
|
| |
