We are given that the area of the triangular faces of a prism is $348 \text{ cm}^2$. Also, $x + 4x + 5x = 348$. We need to find the value of $x$, which represents the length of the prism.

1. Problem Description

We are given that the area of the triangular faces of a prism is $348 \text{ cm}^2$. Also, $x + 4x + 5x = 348$. We need to find the value of $x$, which represents the length of the prism.

2. Solution Steps

The given equation is $x + 4x + 5x = 348$.

Combine the terms on the left side:

$1x + 4x + 5x = (1+4+5)x = 10x$.

So we have $10x = 348$.

To solve for $x$, divide both sides by $10$:

$x = \frac{348}{10} = 34.8$

The value of $x$ is $34.8 \text{ cm}$.

The student has written the equation $x+4x+5x=348$.

Then combined the terms as $12x = 348$.

So $x=\frac{348}{12}=29$.

$3x - y = 7$

$5x + 9 = 25$. We are asked to find $x+y$.

From $5x+9=25$, we can find $x$:

$5x = 25-9=16$

$x = \frac{16}{5} = 3.2$

Substitute $x = 3.2$ into $3x-y=7$:

$3(3.2) - y = 7$

$9.6 - y = 7$

$y = 9.6 - 7$

$y = 2.6$

Now find $x+y$:

$x+y = 3.2 + 2.6 = 5.8$

3. Final Answer

The length of the prism is 29 cm.

The value of $x+y = 5.8$.