Surface Area of Cuboid: Find X When Area = 98 (Given Sides 4 and 9)

To solve this problem, we'll follow these steps:

• Step 1: Substitute the known values into the surface area formula.

• Step 2: Simplify the equation to solve for the unknown $X$.

• Step 3: Perform the necessary calculations to find $X$.

Now, let's work through each step:
Step 1: The given formula for the surface area of a cuboid is $A = 2(lw + lh + wh)$. Here, $l = X$, $w = 4$, and $h = 9$. The surface area is 98.
Step 2: Substitute into the formula:
$98 = 2(X \cdot 4 + X \cdot 9 + 4 \cdot 9)$.
Simplify the expression:
$98 = 2(4X + 9X + 36)$.
$98 = 2(13X + 36)$.
Next, expand the equation:
$98 = 26X + 72$.
Step 3: Solve for $X$:
Subtract 72 from both sides:
$98 - 72 = 26X$.
$26 = 26X$.
Divide both sides by 26:
$X = \frac{26}{26}$.
Therefore, $X = 1$.

In conclusion, the value of $X$ is $1$.