Find the type 0f triangle with sides 4,5,6 cm

Answer

To determine the type of triangle formed by the sides measuring 4 cm, 5 cm, and 6 cm, we can follow these steps:

### Step 1: Identify the sides of the triangle
Let the sides of the triangle be:
- \( a = 4 \) cm
- \( b = 5 \) cm
- \( c = 6 \) cm

### Step 2: Calculate the squares of the sides
Now, we will calculate the squares of each side:
- \( a^2 = 4^2 = 16 \)
- \( b^2 = 5^2 = 25 \)
- \( c^2 = 6^2 = 36 \)

### Step 3: Compare the sum of the squares of the two shorter sides with the square of the longest side
Next, we need to check the relationship between the squares:
- Calculate \( a^2 + b^2 \):
\[ a^2 + b^2 = 16 + 25 = 41 \]
- Now, compare \( a^2 + b^2 \) with \( c^2 \):
\[ a^2 + b^2 = 41 \quad \text{and} \quad c^2 = 36 \]

### Step 4: Determine the type of triangle
Now we analyze the comparison:
- Since \( a^2 + b^2 > c^2 \) (41 > 36), this means that the triangle is an **acute triangle**.

### Conclusion
The triangle with sides 4 cm, 5 cm, and 6 cm is an **acute triangle**.

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