A FARMER BUILT A PEN FOR HIS FAVORITE PIG. THE PEN SHOWN BELOW HAS AN AREA OF 50 SQUARE FEET.THE PEN IS TWICE AS WIDE AS IT IS LONG AND HAS A PERIMETER OF 30 FEET. WHAT IS THE LENGTH, IN FEET OF THE PEN.
P = 2L + 2W
30 = 2L + 4L
30 = 6L
5 = L
2 * 5 = W
W=10
To find the length of the pen, we can first set up a system of equations based on the given information.
Let's denote the length of the pen as "L" and the width as "W".
Based on the given information, we can form the following equations:
1. The area of the pen is 50 square feet:
A = L * W = 50
2. The pen is twice as wide as it is long:
W = 2L
3. The perimeter of the pen is 30 feet:
P = 2L + 2W = 30
Now, we can solve this system of equations to find the length of the pen.
Substituting equation 2 into equation 1, we get:
L * (2L) = 50
2L^2 = 50
L^2 = 25
L = √25
L = 5
Therefore, the length of the pen is 5 feet.