If sides of a triangle are 20 cm, 16 cm and 13 cm, then which one of the following is true ?

Options

A. triangle is obtuse angled
B. triangle is equiangular
C. triangle is acute angled
D. connot known

Answer

To determine the type of triangle formed by the sides measuring 20 cm, 16 cm, and 13 cm, we can follow these steps:

### Step 1: Identify the sides of the triangle
We have three sides:
- Side a = 16 cm
- Side b = 13 cm
- Side c = 20 cm (the longest side)

### Step 2: Apply the Pythagorean theorem
To classify the triangle, we will use the Pythagorean theorem. According to this theorem:
- If \( c^2 = a^2 + b^2 \), the triangle is a right triangle.
- If \( c^2 < a^2 + b^2 \), the triangle is an acute triangle.
- If \( c^2 > a^2 + b^2 \), the triangle is an obtuse triangle.

### Step 3: Calculate \( c^2 \)
Calculate \( c^2 \):
\[ c^2 = 20^2 = 400 \text{ cm}^2 \]

### Step 4: Calculate \( a^2 + b^2 \)
Now calculate \( a^2 + b^2 \):
\[ a^2 = 16^2 = 256 \text{ cm}^2 \]
\[ b^2 = 13^2 = 169 \text{ cm}^2 \]
\[ a^2 + b^2 = 256 + 169 = 425 \text{ cm}^2 \]

### Step 5: Compare \( c^2 \) and \( a^2 + b^2 \)
Now we compare \( c^2 \) and \( a^2 + b^2 \):
\[ c^2 = 400 \text{ cm}^2 \]
\[ a^2 + b^2 = 425 \text{ cm}^2 \]

Since \( c^2 < a^2 + b^2 \):
\[ 400 < 425 \]

### Step 6: Conclusion
Since \( c^2 < a^2 + b^2 \), we conclude that the triangle is an **acute triangle**.

### Final Answer
The correct option is that the triangle is an acute triangle.

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