A farmer wishes to fence a rectangular area behind his barn. The barn forms one end of the rectangle and the length of the rectangle is three times the width. How many linear feet of fence must he buy if the perimeter of the rectangle is 320 feet?
The possible solutions are ___ or ___ linear feet.
How do you answer the possible solutions......
To solve this problem, we need to set up an equation based on the given information.
Let's assume that the width of the rectangle is "w" feet.
According to the problem, the length of the rectangle is three times the width, so the length would be 3w feet.
The perimeter of a rectangle is given by the formula P = 2(l + w), where P represents the perimeter, l represents the length, and w represents the width.
So, in this case, the equation would be:
320 = 2(3w + w)
Simplifying the equation, we get:
320 = 2(4w)
Dividing both sides of the equation by 2:
160 = 4w
Now, we can solve for w:
w = 160/4
w = 40
So, the width of the rectangle is 40 feet.
Since the length of the rectangle is three times the width, the length would be:
l = 3w = 3(40) = 120
Therefore, the length of the rectangle is 120 feet.
To find the total linear feet of fence, we need to calculate the perimeter of the rectangle:
Perimeter = 2(l + w)
= 2(120 + 40)
= 2(160)
= 320
Hence, the farmer needs to buy 320 feet of fence.
What Anonymous said.
Width = W.
Length = 3W.
2W + 2L = 320.
2W + 2*3W = 320,
W = 40 Ft. = Width.
Length = 3W = 3*40 = 120 Ft.
Since the barn forms one end of the rectangle, we only need W + 2L:
W + 2L = 40 + 2*120 = 280 Ft.