Question

which of the following sets of numbers represents the three sides of a right triangle?
○ 1, 2, $sqrt{5}$
○ 3, 4, 6
○ 14, 22, 26
○ 9, 11, 15

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Test 1, 2, $\sqrt{5}$

$1^2 + 2^2 = 1 + 4 = 5$, $(\sqrt{5})^2 = 5$. $5=5$, satisfies theorem.

Step3: Test 3, 4, 6

$3^2 + 4^2 = 9 + 16 = 25$, $6^2 = 36$. $25
eq36$, fails.

Step4: Test 14, 22, 26

$14^2 + 22^2 = 196 + 484 = 680$, $26^2 = 676$. $680
eq676$, fails.

Step5: Test 9, 11, 15

$9^2 + 11^2 = 81 + 121 = 202$, $15^2 = 225$. $202
eq225$, fails.

Answer:

1, 2, $\sqrt{5}$