A rectangular 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

Answer:

the value of x is:

x = 3/2