Farmer wants to enclose a rectangular area that is 600 sq. ft. He is using his barn for one of the sides. The barn is 30 feet long and he does not want the pen to extend longer than the barn. How much fencing will need to be purchased?
so let the width be x , we know the length is 30
30x = 600
x = 20
so he needs 20+20+30 = 70 ft
To determine the amount of fencing needed, we need to find the perimeter of the rectangular area that the farmer wants to enclose.
Let's denote the length of the rectangular area as L and the width as W.
We know that the area of the rectangle is 600 sq. ft., so we have the equation L * W = 600.
Since the barn will be used as one of the sides of the rectangle, its length will be equal to the width of the rectangle (W).
Given that the barn's length is 30 feet, we can substitute W = 30 into the equation above:
L * 30 = 600.
Now, we can solve for L by dividing both sides of the equation by 30:
L = 600 / 30,
L = 20.
Therefore, the length of the rectangular area is 20 feet.
To find the perimeter, we use the formula P = 2L + 2W:
P = 2 * L + 2 * W,
P = 2 * 20 + 2 * 30,
P = 40 + 60,
P = 100.
Therefore, the farmer will need to purchase 100 feet of fencing to enclose the rectangular area.