Question

5 multiple choice 20 points the pythagorean theorem given: a = 3 and b = 9 what does c equal? 3√10 2√10 6√5 3√5

Explanation:

Step1: Substitute values into formula

Given $a = 3$, $b = 9$ and the Pythagorean theorem $a^{2}+b^{2}=c^{2}$, we substitute to get $3^{2}+9^{2}=c^{2}$.

Step2: Calculate left - hand side

$3^{2}=9$, $9^{2}=81$, so $9 + 81=c^{2}$, which simplifies to $c^{2}=90$.

Step3: Solve for c

Taking the square root of both sides, $c=\sqrt{90}$. Simplifying $\sqrt{90}=\sqrt{9\times10}=3\sqrt{10}$.

Answer:

$3\sqrt{10}$