What is the length of a cuboid having breadth and height equal to 4 cm and 6 cm respectively , and the total surface area of `148 cm^(2)` ?

Answer

To find the length of the cuboid given the breadth, height, and total surface area, we can follow these steps:

### Step 1: Write down the formula for the total surface area of a cuboid.
The formula for the total surface area (TSA) of a cuboid is:
\[ \text{TSA} = 2(lb + bh + hl) \]
where \( l \) is the length, \( b \) is the breadth, and \( h \) is the height.

### Step 2: Substitute the known values into the formula.
Given:
- Breadth \( b = 4 \, \text{cm} \)
- Height \( h = 6 \, \text{cm} \)
- Total Surface Area \( \text{TSA} = 148 \, \text{cm}^2 \)

Substituting these values into the formula:
\[ 148 = 2(l \cdot 4 + 4 \cdot 6 + 6 \cdot l) \]

### Step 3: Simplify the equation.
First, divide both sides by 2:
\[ 74 = l \cdot 4 + 24 + 6l \]
Now, combine like terms:
\[ 74 = 4l + 6l + 24 \]
\[ 74 = 10l + 24 \]

### Step 4: Isolate the variable \( l \).
Subtract 24 from both sides:
\[ 74 - 24 = 10l \]
\[ 50 = 10l \]
Now, divide both sides by 10:
\[ l = \frac{50}{10} \]
\[ l = 5 \, \text{cm} \]

### Final Answer:
The length of the cuboid is \( 5 \, \text{cm} \).

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