Question

3 multiple choice 1 point
which set of lengths could not form a right triangle?
21, 28, 49
6, 9, $3\sqrt{13}$
8, 15, 17
65, 72, 97

Explanation:

Step1: Recall Pythagorean theorem

For right triangle: $a^2 + b^2 = c^2$, $c$ is longest side.

Step2: Test option A

$21^2 + 28^2 = 441 + 784 = 1225$; $49^2 = 2401$. $1225
eq 2401$

Step3: Verify other options (confirm validity)

Option B: $6^2 + 9^2 = 36 + 81 = 117$; $(3\sqrt{13})^2 = 9*13=117$. Equal, valid.
Option C: $8^2 +15^2=64+225=289$; $17^2=289$. Equal, valid.
Option D: $65^2 +72^2=4225+5184=9409$; $97^2=9409$. Equal, valid.

Answer:

A. 21, 28, 49