Answer: The height is 9 feet.
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