The edges of a cuboid are in the ratio `1 : 2 : 3` and its surface area is 88 `cm^2`. Find the length, breadth and height respectively of cuboid.

Options

A. 2, 4 and 6
B. 4, 8 and 2
C. 6, 4 and 2
D. 8, 2 and 6

Answer

To solve the problem step by step, we will follow the given information about the cuboid's dimensions and surface area.

### Step-by-Step Solution:

1. **Understanding the Ratios**:
The edges of the cuboid are in the ratio 1:2:3. Let's denote:
- Length (L) = \( x \)
- Breadth (B) = \( 2x \)
- Height (H) = \( 3x \)

2. **Surface Area Formula**:
The formula for the surface area (SA) of a cuboid is given by:
\[ SA = 2(LB + BH + LH) \]

3. **Substituting the Values**:
Substitute the values of L, B, and H into the surface area formula:
\[ SA = 2(x \cdot 2x + 2x \cdot 3x + 3x \cdot x) \]
Simplifying this:
\[ SA = 2(2x^2 + 6x^2 + 3x^2) = 2(11x^2) = 22x^2 \]

4. **Setting Up the Equation**:
We know the surface area is 88 cm², so we set up the equation:
\[ 22x^2 = 88 \]

5. **Solving for x**:
Divide both sides by 22:
\[ x^2 = \frac{88}{22} = 4 \]
Now, take the square root of both sides:
\[ x = \sqrt{4} = 2 \]

6. **Finding Length, Breadth, and Height**:
Now that we have \( x \), we can find the dimensions:
- Length (L) = \( x = 2 \) cm
- Breadth (B) = \( 2x = 2 \cdot 2 = 4 \) cm
- Height (H) = \( 3x = 3 \cdot 2 = 6 \) cm

### Final Answer:
The dimensions of the cuboid are:
- Length = 2 cm
- Breadth = 4 cm
- Height = 6 cm