The perimeter of a triangle is 115 cm. If two of its sides are 35 cm and 37 cm. Find the third side of the triangle.

Options

A. 43 cm
B. 73 cm
C. 35 cm
D. 37 cm

Answer

To find the third side of the triangle given the perimeter and the lengths of the other two sides, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the formula for the perimeter of a triangle**:
The perimeter (P) of a triangle is the sum of the lengths of all its sides. If we denote the sides of the triangle as \( AB \), \( BC \), and \( CA \), then:
\[ P = AB + BC + CA \]

2. **Substitute the known values into the perimeter formula**:
We know the perimeter is 115 cm, and two sides are given as 35 cm and 37 cm. Let's denote:
- \( AB = 35 \) cm
- \( BC = 37 \) cm
- \( CA = ? \) (the side we need to find)

So, we can write:
\[ 115 = 35 + 37 + CA \]

3. **Combine the known side lengths**:
First, we need to add the lengths of the two known sides:
\[ 35 + 37 = 72 \]

4. **Set up the equation to find the unknown side**:
Now we can substitute this sum back into the equation:
\[ 115 = 72 + CA \]

5. **Isolate the unknown side (CA)**:
To find \( CA \), we can rearrange the equation:
\[ CA = 115 - 72 \]

6. **Calculate the value of CA**:
Now, we perform the subtraction:
\[ CA = 43 \text{ cm} \]

### Final Answer:
The length of the third side of the triangle is **43 cm**.

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