Question

triangle classification theorems
which best explains whether a triangle with side lengths 5 cm, 13 cm, and 12 cm is a right triangle?
the triangle is a right triangle because $5^2 + 12^2 = 13^2$.
the triangle is not a right triangle because $5^2 + 13^2 > 12^2$.
the triangle is not a right triangle because $5 + 12 > 13$.
the triangle is a right triangle because $5 + 13 > 12$.

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Identify sides and assign values

Longest side $c=13$, $a=5$, $b=12$.

Step3: Calculate left-hand side

$5^2 + 12^2 = 25 + 144 = 169$

Step4: Calculate right-hand side

$13^2 = 169$

Step5: Compare both sides

$169 = 169$, so the theorem holds.

Answer:

The triangle is a right triangle because $5^2 + 12^2 = 13^2$.