Question

question
which of the following sets of numbers could not represent the three sides of a right triangle?
answer
○ {5,8,10}
○ {12,35,37}
○ {12,16,20}
○ {33,56,65}
submit answer

Explanation:

Step1: Check Pythagorean theorem for set 1

For $\{5,8,10\}$, test $5^2 + 8^2 = 10^2$

$$\begin{aligned} 5^2 + 8^2 &= 25 + 64 = 89 \\ 10^2 &= 100 \end{aligned}$$

$89
eq 100$, so not a right triangle.

Step2: Verify other sets (confirmation)

For $\{12,16,20\}$: $12^2+16^2=144+256=400=20^2$
For $\{12,35,37\}$: $12^2+35^2=144+1225=1369=37^2$
For $\{33,56,65\}$: $33^2+56^2=1089+3136=4225=65^2$

Answer:

$\{5, 8, 10\}$