Calculate Cuboid Length: Given Surface Area 124 cm²

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

• Step 1: Identify the given information and relevant formula
• Step 2: Substitute the known values into the formula
• Step 3: Solve for the unknown variable (length)

Now, let's work through each step:

Step 1: Given the surface area of the cuboid is 124 cm², the width $w = 4$ cm, and the height $h = 2$ cm, we need to find the length $l$. The formula for the surface area of a cuboid is:

$2(lw + lh + wh) = \text{Surface Area}$

Step 2: Substitute the values into the equation:

$2(l \cdot 4 + l \cdot 2 + 4 \cdot 2) = 124$

Which simplifies to:

$2(4l + 2l + 8) = 124$

$2(6l + 8) = 124$

Step 3: Solve for $l$:

First, divide both sides by 2 to simplify:

$6l + 8 = 62$

Subtract 8 from both sides:

$6l = 54$

Divide by 6:

$l = 9$

Therefore, the length of the cuboid is $9$ cm.