Question

solve for c

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs $a = 5$ and $b = 12$, and hypotenuse $c$, the Pythagorean theorem is $a^{2}+b^{2}=c^{2}$. So, $5^{2}+12^{2}=c^{2}$.

Step2: Calculate squares

$5^{2}=25$ and $12^{2}=144$. Then $25 + 144=c^{2}$, so $c^{2}=169$.

Step3: Find the square - root

Taking the square - root of both sides, $c=\sqrt{169}$. Since $c$ represents the length of a side of a triangle and must be positive, $c = 13$.

Answer:

13