Arectangular garden originally measured 5 feet by 10 feet as shown below. a path was created by increasing each side of the original rectangle by x-feet on both sides. if the area of the path that rings the garden is 54 square feet, find the value of x.

The area is given by
 A = (5 + 2x) * (10 + 2x) - 50
 Rewriting we have:
 A = 50 + 10x + 20x + 4x ^ 2 -50
 Rewriting we have:
 A = 4x ^ 2 + 30x
 Substituting the value of the area we have:
 54 = 4x ^ 2 + 30x
 Rewriting:
 4x ^ 2 + 30x - 54 = 0
 We look for the roots:
 x1 = -9
 x2 = 3/2
 We take the positive root:
 x2 = 3/2
 
 the value of x is:
 x = 3/2

The decimal expansion would be .27 repeated