Question

Determine if the numbers given is a right triangle?

1. 5, 12, 15
2. 9, 15, 17
3. 35, 45,55

Answer 1

Based on these calculations, only the numbers 5, 12, 15 form a right triangle.

The answer is option ⇒1

Step-by-step explanation:

To determine if the given numbers form a right triangle, we need to check if they satisfy the Pythagorean theorem. According to the theorem, in a right 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.

Let's check each set of numbers:

1. For the numbers 5, 12, 15:

• - The square of the length of the hypotenuse (15) is 225.
• - The sum of the squares of the other two sides (5²+ 12²= 25 + 144 = 169) is also 169.
• - Since 225 is equal to 169, these numbers satisfy the Pythagorean theorem.
• - Therefore, the numbers 5, 12, 15 form a right triangle.

2. For the numbers 9, 15, 17:

• - The square of the length of the hypotenuse (17) is 289.
• - The sum of the squares of the other two sides (9² + 15² = 81 + 225 = 306) is not equal to 289.
• - Since 289 is not equal to 306, these numbers do not satisfy the Pythagorean theorem.
• - Therefore, the numbers 9, 15, 17 do not form a right triangle.

3. For the numbers 35, 45, 55:

• - The square of the length of the hypotenuse (55) is 3025.
• - The sum of the squares of the other two sides (35² + 45² = 1225 + 2025 = 3250) is not equal to 3025.
• - Since 3025 is not equal to 3250, these numbers do not satisfy the Pythagorean theorem.
• - Therefore, the numbers 35, 45, 55 do not form a right triangle.

Therefore, only the numbers 5, 12, 15 form a right triangle.

The answer is option ⇒1