John made a rectangular pen for his dog using 28 feet of fencing.If the width of the pen is 2 feet more than one-half the length,what are the length and width of the pen?
To find the length and width of the rectangular pen, we can use the given information and set up an equation based on the given conditions.
Let's assume the length of the pen is "L" and the width is "W".
According to the problem, the width of the pen is 2 feet more than one-half the length, which can be expressed as:
W = (1/2)L + 2
The perimeter of a rectangular pen is calculated by summing the lengths of all four sides. In this case, since we are given 28 feet of fencing, we can set up an equation for the perimeter:
Perimeter = 2L + 2W
Substituting the value of W from the previous equation, we get:
28 = 2L + 2((1/2)L + 2)
Simplifying the equation further:
28 = 2L + L + 4
Combining like terms:
28 = 3L + 4
Subtracting 4 from both sides:
24 = 3L
Dividing both sides by 3:
L = 8
Now, we can substitute the value of L back into the equation for W:
W = (1/2)L + 2
W = (1/2)(8) + 2
W = 4 + 2
W = 6
Therefore, the length of the pen is 8 feet, and the width is 6 feet.