Farmer Hodges has 50 feet of fencing to make a rectangular hog pen beside a very large barn. He needs to fence only three sides because the barn will form the fourth side. Studies have shown that under those conditions the side parallel to the barn should be 5 feet longer than twice the width. If farmer Hodges uses all of the fencing, what should the dimensions be?
let the width be x ft
length is 2x+5
we need 2 widths and one length
2x+5 + x + x = 50
4x = 45
x = 45/4 = 11.25 ft
width = 11.25
length = 27.50
To find the dimensions of the hog pen, we need to set up an equation using the given information.
Let's assume that the width of the rectangular hog pen is represented by the variable "w". Since the length ("5 feet longer than twice the width") is dependent on the width, we can represent the length as "2w + 5".
We know that the perimeter of a rectangle is given by the sum of all its sides. In this case, the perimeter is equal to the total length of the fencing, which is 50 feet.
The perimeter of the hog pen can be calculated by adding the length, width, and width together:
Perimeter = Length + Width + Width
Substituting in our length and width expressions:
50 = (2w + 5) + w + w
Simplifying the equation:
50 = 4w + 5
Subtracting 5 from both sides:
50 - 5 = 4w
45 = 4w
Dividing both sides by 4:
w = 45 / 4
So, the width of the hog pen is approximately 11.25 feet.
To find the length, we substitute the value of the width into the expression for the length:
Length = 2w + 5
Length = 2(11.25) + 5
Length = 22.5 + 5
Length = 27.5
Therefore, the dimensions of the hog pen that Farmer Hodges should use are approximately 11.25 feet by 27.5 feet.
Let's denote the width of the rectangular hog pen as "x" feet.
According to the given information, the side parallel to the barn should be 5 feet longer than twice the width. So, the length of the pen would be (2x + 5) feet.
Since the barn forms the fourth side, we only need to fence three sides. This means, we need to fence two sides with the length equal to x feet, and one side with the length equal to (2x + 5) feet.
The total fencing required would be the sum of the lengths of these three sides:
2x + 2x + 5 + x = 50
Combining like terms:
5x + 5 = 50
Subtracting 5 from both sides:
5x = 45
Dividing both sides by 5:
x = 9
Hence, the width of the hog pen is 9 feet.
Now, we can find the length of the hog pen:
Length = 2x + 5 = 2(9) + 5 = 18 + 5 = 23
Therefore, the dimensions of the hog pen should be a width of 9 feet and a length of 23 feet.