Question

which classification best represents a triangle with side lengths 6 cm, 10 cm, and 12 cm?
obtuse, because $6^2 + 10^2 < 12^2$
acute, because $6 + 10 > 12$
acute, because $6^2 + 10^2 < 12^2$
obtuse, because $6 + 10 > 12$

Explanation:

Step1: Recall triangle type rule

For a triangle with sides $a \leq b < c$, if $a^2 + b^2 < c^2$, it is obtuse.

Step2: Calculate each squared side

$6^2=36$, $10^2=100$, $12^2=144$

Step3: Sum smaller squared sides

$36 + 100 = 136$

Step4: Compare to largest squared side

$136 < 144$, so $6^2+10^2<12^2$, triangle is obtuse.

Answer:

A. obtuse, because $6^{2}+10^{2}<12^{2}$