a/ai refrigerator comes packaged in a box shaped ilke a rectangular prism. The base of the box measures 5 feet by 5.5 feet. The total surface area of the box is 186.25 square feet. What is the helght of the box in feet? Enter the decimal answer without units.

To determine the height of the box, we start by using the formula for the surface area of a rectangular prism: \[ \text{Surface Area} = 2(lw + lh + wh) \] Here, \( l = 5 \, \text{ft} \) (length), \( w = 5.5 \, \text{ft} \) (width), and \( h \) is the height we want to find. The surface area is given as 186.25 square feet. First, we compute the area of the base: \[ lw = 5 \times 5.5 = 27.5 \, \text{square feet} \] Now, substituting into the surface area formula: \[ 186.25 = 2(27.5 + 5h + 5.5h) \] Simplifying this gives: \[ 186.25 = 2(27.5 + 11.5h) \] Dividing both sides by 2: \[ 93.125 = 27.5 + 11.5h \] Now, solving for \( h \): \[ 93.125 - 27.5 = 11.5h \] \[ 65.625 = 11.5h \] \[ h = \frac{65.625}{11.5} \] \[ h \approx 5.71 \] Thus, the height of the box is approximately **5.71** feet.