Which of the following are the dimensions of a right triangle ?

Options

A. 0. 6, 0.8,0.12
B. 2,3,4
C. `9, 12, 15`
D. `9, 13, 21`

Answer

To determine which of the given options represent the dimensions of a right triangle, we will apply the Pythagorean theorem. The theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the lengths of the other two sides (the perpendicular and the base).

Let's evaluate each option step by step.

### Step 1: Check Option A - (0.6, 0.8, 0.12)

1. Identify the hypotenuse: The longest side is 0.8.
2. Apply the Pythagorean theorem:
- \(0.8^2 = 0.6^2 + 0.12^2\)
- Calculate: \(0.64 = 0.36 + 0.0144\)
- \(0.64 = 0.3744\) (not equal)

**Conclusion**: Option A does not satisfy the Pythagorean theorem.

### Step 2: Check Option B - (2, 3, 4)

1. Identify the hypotenuse: The longest side is 4.
2. Apply the Pythagorean theorem:
- \(4^2 = 2^2 + 3^2\)
- Calculate: \(16 = 4 + 9\)
- \(16 = 13\) (not equal)

**Conclusion**: Option B does not satisfy the Pythagorean theorem.

### Step 3: Check Option C - (9, 12, 15)

1. Identify the hypotenuse: The longest side is 15.
2. Apply the Pythagorean theorem:
- \(15^2 = 9^2 + 12^2\)
- Calculate: \(225 = 81 + 144\)
- \(225 = 225\) (equal)

**Conclusion**: Option C satisfies the Pythagorean theorem.

### Step 4: Check Option D - (9, 13, 21)

1. Identify the hypotenuse: The longest side is 21.
2. Apply the Pythagorean theorem:
- \(21^2 = 9^2 + 13^2\)
- Calculate: \(441 = 81 + 169\)
- \(441 = 250\) (not equal)

**Conclusion**: Option D does not satisfy the Pythagorean theorem.

### Final Answer:
Only **Option C (9, 12, 15)** represents the dimensions of a right triangle.

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