Based on the converse of the Pythagorean Theorem, which of the following sets of side lengths is NOT a right triangle?

Question

Hint: Does ?
A
62+82=1026
2
+8
2
=10
2

B
22+32=422
2
+3
2
=4
2

C
32+42=523
2
+4
2
=5
2

Answer 1

To determine which of the given sets of side lengths does NOT form a right triangle based on the converse of the Pythagorean Theorem, we need to check if the squares of the two shorter sides equal the square of the longest side for each set.

1. Set A: \( 6, 8, 10 \)

   \[ 6^2 + 8^2 = 36 + 64 = 100 \] \[ 10^2 = 100 \] Since \( 36 + 64 = 100 \), Set A is a right triangle.

2. Set B: \( 2, 3, 4 \)

   \[ 2^2 + 3^2 = 4 + 9 = 13 \] \[ 4^2 = 16 \] Since \( 4 + 9 \neq 16 \), Set B is NOT a right triangle.

3. Set C: \( 3, 4, 5 \)

   \[ 3^2 + 4^2 = 9 + 16 = 25 \] \[ 5^2 = 25 \] Since \( 9 + 16 = 25 \), Set C is a right triangle.

Based on this analysis, the set of side lengths that does NOT form a right triangle is Set B: \( 2, 3, 4 \).