Question

What measurement below does not represent the side lengths of a right triangle?

1) 3, 4, 5
2) 5, 12, 13
3) 6, 8, 10
4) 7, 24, 25

Answer 1

Option 4) 7, 24, 25 does not represent the side lengths of a right triangle.

Step-by-step explanation:

A right triangle is a triangle with one angle measuring 90 degrees.

In a right triangle, the lengths of the three sides follow a specific relationship called the Pythagorean theorem, which states that 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.

So, to determine which of the given options does not represent the side lengths of a right triangle, we can check if the Pythagorean theorem holds true for each option.

1. For option 1) 3, 4, 5:
   3² + 4² = 9 + 16 = 25, which is equal to 5². The Pythagorean theorem holds true for this option.
2. For option 2) 5, 12, 13:
   5² + 12² = 25 + 144 = 169, which is equal to 13². The Pythagorean theorem holds true for this option.
3. For option 3) 6, 8, 10:
   6² + 8² = 36 + 64 = 100, which is equal to 10². The Pythagorean theorem holds true for this option.
4. For option 4) 7, 24, 25:
   7² + 24² = 49 + 576 = 625, which is not equal to 25². The Pythagorean theorem does not hold true for this option.

Therefore, the measurement 7, 24, 25 does not represent the side lengths of a right triangle.