The sides of a triangle are in the ratio `12:15:20:` If its perimeter be 94 cm, find the length of smallest side of the triangle.

Options

A. 18 cm
B. 22.5 cm
C. 24 cm
D. 27 cm

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 12:15:20. We can represent the sides of the triangle as:
- Side 1 = 12x
- Side 2 = 15x
- Side 3 = 20x

### Step 2: Write the equation for the perimeter
The perimeter of a triangle is the sum of all its sides. Therefore, we can write the equation for the perimeter as follows:
\[ \text{Perimeter} = 12x + 15x + 20x \]

### Step 3: Simplify the perimeter equation
Now, we can combine the terms:
\[ \text{Perimeter} = (12 + 15 + 20)x = 47x \]

### Step 4: Set the perimeter equal to the given value
We know that the perimeter is 94 cm, so we can set up the equation:
\[ 47x = 94 \]

### Step 5: Solve for x
To find the value of x, we will divide both sides of the equation by 47:
\[ x = \frac{94}{47} = 2 \]

### Step 6: Find the lengths of the sides
Now that we have the value of x, we can find the lengths of the sides:
- Side 1 = 12x = 12 * 2 = 24 cm
- Side 2 = 15x = 15 * 2 = 30 cm
- Side 3 = 20x = 20 * 2 = 40 cm

### Step 7: Identify the smallest side
Among the sides 24 cm, 30 cm, and 40 cm, the smallest side is:
- Smallest side = 24 cm

### Final Answer
The length of the smallest side of the triangle is **24 cm**.

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