Question

James and Ryan are working on math problems. James insists that this is the right triangle can be formed with a side length of 6, 8 and 14 because 6+8 = 14. Ryan argues that he's a correct explain where he went wrong in a complete sentence.

Answer 1

Ryan is correct. The side lengths of 6, 8, and 14 cannot form a right triangle because of the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides. If we apply this theorem to the side lengths of 6, 8, and 14, we get:

6^2 + 8^2 = 36 + 64 = 100

14^2 = 196

Since 196 is not equal to 100, these side lengths do not satisfy the Pythagorean theorem and cannot form a right triangle. Therefore, James is mistaken in thinking that a right triangle can be formed with these side lengths based solely on the sum of two of the sides.