Question

The surface of the prism is 298 square feet Find the value of x

Answer 1

The rectangular prisma has 6 faces. The area of the front and back faces is

`\begin{gathered} A_1=2*(7* x) \\ A_1=14x \end{gathered}`

The area of the base faces is

`\begin{gathered} A_2=2*7*4 \\ A_2=56 \end{gathered}`

and the area of the lateral faces is

`\begin{gathered} A_3=2*4* x \\ A_3=8x \end{gathered}`

Then, the total surface area is the sum of the above results, that is,

`\begin{gathered} S=A_1+A_2+A_3 \\ S=14x+56+8x \end{gathered}`

By combining similar terms, it gives

`S=22x+56`

Now, from the given information, we know that the surface area must be equal to 298 square feet. So, we have

`22x+56=298`

Then, by subtracting 56 to both sides, we have

`\begin{gathered} 22x=298-56 \\ 22x=242 \end{gathered}`

and by dividing both sides by 22, we get

`\begin{gathered} x=(242)/(22) \\ x=11 \end{gathered}`

Therefore, the answer is 11 feet