The perimeter of the rectangle = 2 * ( length + width )
So,
The perimeter of the given rectangle
= 2 * ( 4 1/4 + n )
But it is given that the perimeter is 23 feet
So,
23 = 2 * ( 4 1/4 + n )
Solve the equation to find n
divide both sides by 2
23/2 = 4 1/4 + n
n = 23/2 - 4 1/4 = 7 1/4
So, the length of the missing side = 7 1/4 feet
The answer is option C. 7 1/4 feet