The sides of a triangle are in the ratio `4:3:2`. If the perimeter of the triangle is 63 cm, then what will be the length of the largest side?

Options

A. 28cm
B. 35cm
C. 21cm
D. 42cm

Answer

To solve the problem, we will follow these steps:

1. **Understand the Ratio of the Sides**: The sides of the triangle are given in the ratio 4:3:2. This means we can express the sides in terms of a variable \( x \). Let the sides be:
- Side 1 = \( 4x \)
- Side 2 = \( 3x \)
- Side 3 = \( 2x \)

2. **Calculate the Perimeter**: The perimeter of the triangle is the sum of its sides. Therefore, we can write:
\[ \text{Perimeter} = 4x + 3x + 2x \]
Simplifying this gives:
\[ \text{Perimeter} = 9x \]

3. **Set Up the Equation**: We know from the problem that the perimeter is 63 cm. Thus, we can set up the equation:
\[ 9x = 63 \]

4. **Solve for \( x \)**: To find \( x \), divide both sides of the equation by 9:
\[ x = \frac{63}{9} = 7 \text{ cm} \]

5. **Find the Length of Each Side**: Now that we have \( x \), we can find the lengths of the sides:
- Side 1 = \( 4x = 4 \times 7 = 28 \text{ cm} \)
- Side 2 = \( 3x = 3 \times 7 = 21 \text{ cm} \)
- Side 3 = \( 2x = 2 \times 7 = 14 \text{ cm} \)

6. **Identify the Largest Side**: From the calculated lengths, the largest side is:
\[ \text{Largest Side} = 28 \text{ cm} \]

Thus, the length of the largest side of the triangle is **28 cm**.