A rectangular prism has a surface area of 286 ft squared. The base is 5ft by 7ft what is the height of the prism?

 The height is 9 feet.

Step-by-step explanation:

The surface area is the total of the areas of the 6 faces of the rectangular prism. Given 286 square feet.

The base given is 5ft by 7ft, so that will give the area of 2 faces;

the other pairs of faces have the unknown height as one factor

5ft by h and 7ft by h .  Create an equation with those factors:

2(5×7) + 2(5h)  + 2(7h) = 286  Distribute and compile

2(35) + 10h + 14h = 286    70 + 24h = 286 .  Solve for h

24h = 286 - 70 .    24h = 216 .  216 ÷ 24 = 9

h = 9

  So the height of the rectangular prism is 9 feet