Two sides of a triangle are 25 cm and 23 cm and semi perimeter of triangle is 30 cm then third side is

Given the information:

- Two sides of the triangle are 25 cm and 23 cm.
- The semi-perimeter \( s \) of the triangle is 30 cm.

We can find the third side of the triangle using the following method.

### Step 1: Understanding the Semi-Perimeter
The semi-perimeter \( s \) of a triangle is given by:
\[
s = \frac{a + b + c}{2}
\]
where \( a \), \( b \), and \( c \) are the sides of the triangle.

### Step 2: Calculate the Third Side
Given:
\[
s = 30 \text{ cm}
\]
\[
a = 25 \text{ cm}, \quad b = 23 \text{ cm}
\]
We need to find \( c \).

Using the formula for the semi-perimeter:
\[
30 = \frac{25 + 23 + c}{2}
\]

### Step 3: Solve for \( c \)
Multiply both sides by 2 to eliminate the fraction:
\[
60 = 25 + 23 + c
\]

Simplify to find \( c \):
\[
60 = 48 + c
\]

\[
c = 60 - 48 = 12 \text{ cm}
\]

### Conclusion
The third side of the triangle is **12 cm**.

Would you like any further details or have any other questions? Here are some related questions:

1. How do you calculate the area of a triangle given three sides?
2. What is Heron's formula, and how is it used in triangle calculations?
3. Can a triangle with sides 12 cm, 25 cm, and 23 cm be a right triangle?
4. How do you determine the type of triangle based on its side lengths?
5. What are the properties of a triangle when one of its angles is obtuse?

**Tip:** Remember, in any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side.

Learn how to find the third side of a triangle when two sides (25 cm and 23 cm) and the semi-perimeter (30 cm) are given. Detailed step-by-step solution with the semi-perimeter formula. Suitable for high school students.

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