Question

2. Which of the following lists of side lengths represents a right triangle?

A) 5, 12, 14
B) 15,16,17
C) 7,24,25​

Answer 1

A right triangle follows the Pythagorean theorem, which states that the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. In other words, a^2 + b^2 = c^2, where a and b are the shorter sides, and c is the hypotenuse.

Let's check each option:

A) 5^2 + 12^2 = 25 + 144 = 169, which is not equal to 14^2 = 196.
B) 15^2 + 16^2 = 225 + 256 = 481, which is not equal to 17^2 = 289.
C) 7^2 + 24^2 = 49 + 576 = 625, which is equal to 25^2 = 625.

So, option C) 7, 24, 25 represents a right triangle.

Answer 2

A) 5, 12, 14

Explanation:

Let's check each option:

A) 5, 12, 14

To see if this forms a right triangle, we can use the Pythagorean theorem:

5^2 + 12^2 = 25 + 144 = 169

14^2 = 196

The sum of the squares of the two shorter sides (25 + 144 = 169) is equal to the square of the longest side (196), so this list of side lengths does represent a right triangle.

B) 15, 16, 17

Applying the Pythagorean theorem:

15^2 + 16^2 = 225 + 256 = 481

17^2 = 289

The sum of the squares of the two shorter sides (225 + 256 = 481) is not equal to the square of the longest side (289). Therefore, this list of side lengths does not represent a right triangle.

C) 7, 24, 25

Using the Pythagorean theorem:

7^2 + 24^2 = 49 + 576 = 625

25^2 = 625

The sum of the squares of the two shorter sides (49 + 576 = 625) is equal to the square of the longest side (625). Hence, this list of side lengths does represent a right triangle.

Therefore, the correct answer is:

A) 5, 12, 14