Question

a triangle has sides with lengths 8 inches, 15 inches, and 17 inches. is the triangle a right triangle? explain how you know

\bigcirc no, because $8 + 15 \
eq 17$.

\bigcirc yes, because $8^2 + 15^2 = 17^2$

\bigcirc no, because $8^2 + 15^2 = 17^2$

\bigcirc no, because $8 + 15 = 17$

Explanation:

Step1: Recall Pythagorean theorem

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

Step2: Calculate $8^2 + 15^2$

$8^2 + 15^2 = 64 + 225 = 289$

Step3: Calculate $17^2$

$17^2 = 289$
Wait, correction: $8^2+15^2=64+225=289$, $17^2=289$, so $8^2+15^2=17^2$. Correct answer: Yes, because $8^2 + 15^2 = 17^2$

Step1: Identify longest side

Longest side is 17 inches.

Step2: Compute sum of squares of shorter sides

$8^2 + 15^2 = 64 + 225 = 289$

Step3: Compute square of longest side

$17^2 = 289$

Step4: Compare the two results

$289 = 289$, so $8^2 + 15^2 = 17^2$

Answer:

No, because $8^2 + 15^2
eq 17^2$