Question

does a² + b² = c² hold true for this right triangle? a = 8 b = 5 c = √89 a² + b² stackrel{?}{=} c² no, a² + b² = c² is not true for this right triangle. yes, a² + b² = c² is true for this right triangle.

Explanation:

Step1: Calculate $a^2$

$a = 8$, so $a^2=8^2 = 64$

Step2: Calculate $b^2$

$b = 5$, so $b^2=5^2 = 25$

Step3: Calculate $c^2$

$c=\sqrt{89}$, so $c^2=(\sqrt{89})^2 = 89$

Step4: Check the Pythagorean theorem

$a^2 + b^2=64 + 25=89$, and $c^2 = 89$. Since $a^2 + b^2=c^2$.

Answer:

Yes, $a^2 + b^2 = c^2$ is true for this right triangle.