The sides of a triangle are in the ratio 1 : 3:5 and its perimeter is 90 cm. The length of its largest side is

Options

A. 40 cm
B. 50 cm
C. 36 cm
D. 54 cm

Answer

To solve the problem step by step, we will follow the reasoning provided in the video transcript.

### Step-by-Step Solution:

1. **Understand the Ratio of the Sides**:
The sides of the triangle are given in the ratio 1 : 3 : 5. This means if we let the sides be represented as:
- Side AB = 1x
- Side BC = 3x
- Side AC = 5x

2. **Set Up the Perimeter Equation**:
The perimeter of a triangle is the sum of all its sides. We know the perimeter is 90 cm. Therefore, we can write the equation:
\[ AB + BC + AC = 90 \text{ cm} \]
Substituting the expressions for the sides:
\[ 1x + 3x + 5x = 90 \]

3. **Combine Like Terms**:
Combine the terms on the left side of the equation:
\[ 9x = 90 \]

4. **Solve for x**:
To find the value of x, divide both sides of the equation by 9:
\[ x = \frac{90}{9} = 10 \]

5. **Calculate the Length of Each Side**:
Now that we have the value of x, we can find the lengths of each side:
- Side AB = 1x = 1 * 10 = 10 cm
- Side BC = 3x = 3 * 10 = 30 cm
- Side AC = 5x = 5 * 10 = 50 cm

6. **Identify the Largest Side**:
Among the sides calculated, we can see:
- AB = 10 cm
- BC = 30 cm
- AC = 50 cm
The largest side is AC, which measures 50 cm.

### Final Answer:
The length of the largest side of the triangle is **50 cm**.

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