The sides of a triangle are in the ratio 3 : 4 : 5 and its perimeter is 72 cm. The length of its greatest side (in cm) is

Options

A. 24
B. 27
C. 30
D. 36

Answer

To solve the problem, we will follow these steps:

### Step 1: Understand the ratio of the sides
The sides of the triangle are given in the ratio of 3:4:5. This means we can represent the sides as:
- Side 1 = 3x
- Side 2 = 4x
- Side 3 = 5x

### Step 2: Set up the equation for the perimeter
The perimeter of a triangle is the sum of all its sides. According to the problem, the perimeter is 72 cm. Therefore, we can write the equation:
\[ 3x + 4x + 5x = 72 \]

### Step 3: Simplify the equation
Combine the terms on the left side:
\[ (3x + 4x + 5x) = 12x \]
So, the equation becomes:
\[ 12x = 72 \]

### Step 4: Solve for x
To find the value of x, divide both sides of the equation by 12:
\[ x = \frac{72}{12} \]
\[ x = 6 \]

### Step 5: Calculate the lengths of the sides
Now that we have the value of x, we can find the lengths of the sides:
- Side 1 = \( 3x = 3 \times 6 = 18 \) cm
- Side 2 = \( 4x = 4 \times 6 = 24 \) cm
- Side 3 = \( 5x = 5 \times 6 = 30 \) cm

### Step 6: Identify the greatest side
Among the calculated sides (18 cm, 24 cm, and 30 cm), the greatest side is:
\[ 30 \text{ cm} \]

### Conclusion
The length of the greatest side of the triangle is **30 cm**.

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