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: Solve for \(c\)

Take the square - root of both sides. Since \(c\) represents the length of a side of a triangle (a non - negative quantity), \(c=\sqrt{169}=13\).

Answer:

13