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

Answer: 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