Which of following does not form a Pythagoras triplet ?

Options

A. (7,24,25)
B. (15,8,17)
C. (5,12,13)
D. (21,20,28)

Answer

To determine which of the given sets of numbers does not form a Pythagorean triplet, we can follow these steps:

### Step 1: Understand the Pythagorean Theorem
The Pythagorean theorem states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed as:
\[ c^2 = a^2 + b^2 \]
where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the other two sides.

### Step 2: Identify the Options
Assume we have the following options:
1. (7, 24, 25)
2. (15, 8, 17)
3. (5, 12, 13)
4. (21, 20, 28)

### Step 3: Check Each Option
We will check each option to see if they satisfy the Pythagorean theorem.

**Option 1: (7, 24, 25)**
- Calculate \( 7^2 + 24^2 \):
\[ 7^2 = 49, \quad 24^2 = 576 \quad \Rightarrow \quad 49 + 576 = 625 \]
- Calculate \( 25^2 \):
\[ 25^2 = 625 \]
- Since \( 49 + 576 = 625 \), this forms a Pythagorean triplet.

**Option 2: (15, 8, 17)**
- Calculate \( 8^2 + 15^2 \):
\[ 8^2 = 64, \quad 15^2 = 225 \quad \Rightarrow \quad 64 + 225 = 289 \]
- Calculate \( 17^2 \):
\[ 17^2 = 289 \]
- Since \( 64 + 225 = 289 \), this forms a Pythagorean triplet.

**Option 3: (5, 12, 13)**
- Calculate \( 5^2 + 12^2 \):
\[ 5^2 = 25, \quad 12^2 = 144 \quad \Rightarrow \quad 25 + 144 = 169 \]
- Calculate \( 13^2 \):
\[ 13^2 = 169 \]
- Since \( 25 + 144 = 169 \), this forms a Pythagorean triplet.

**Option 4: (21, 20, 28)**
- Calculate \( 21^2 + 20^2 \):
\[ 21^2 = 441, \quad 20^2 = 400 \quad \Rightarrow \quad 441 + 400 = 841 \]
- Calculate \( 28^2 \):
\[ 28^2 = 784 \]
- Since \( 441 + 400 = 841 \) is not equal to \( 784 \), this does not form a Pythagorean triplet.

### Conclusion
The set of numbers that does not form a Pythagorean triplet is **(21, 20, 28)**.

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