Surface Area of a Cuboid: Find X When Area = 284 cm²

To solve for $X$, we begin with the formula for the surface area of a cuboid:

$A = 2(ab + bc + ca)$, where $a = 10$, $b = (X - 3)$, and $c = 12$.

Substitute the given surface area into the formula:

$284 = 2((10)(X-3) + (X-3)(12) + (10)(12))$

Simplify the equation by first expanding each term inside the parentheses:

$284 = 2(10X - 30 + 12X - 36 + 120)$

Combine like terms:

$284 = 2(22X + 54)$

Divide both sides by 2 to isolate the linear expression:

$142 = 22X + 54$

Subtract 54 from both sides to solve for $22X$:

$88 = 22X$

Finally, divide by 22 to find $X$:

$X = \frac{88}{22} = 4$

Therefore, the solution to the problem is $X = 4$.