Surface Area 292: Solve for X in a Cuboid with Dimensions (X+4), 7, and 8

To find $X$, follow these steps:

• Step 1: Apply the formula for the surface area of a cuboid: $SA = 2(lw + lh + wh)$.
• Step 2: Substitute the given dimensions: $(X+4)$, $7$, and $8$.
• Step 3: Set up the equation given $SA = 292$.

Using the surface area formula:

$SA = 2\left((X+4) \times 7 + (X+4) \times 8 + 7 \times 8\right) = 292$

Calculate each part:

$(X+4) \times 7 = 7X + 28$

$(X+4) \times 8 = 8X + 32$

$7 \times 8 = 56$

Combine and simplify:

$7X + 28 + 8X + 32 + 56 = 15X + 116$

Use the equation for surface area:

$2(15X + 116) = 292$

$30X + 232 = 292$

Simplifying further:

$30X = 292 - 232$

$30X = 60$

$X = \frac{60}{30}$

$X = 2$

Therefore, the value of $X$ is $2$.