Question

for the following right triangle, find the side length x. your answer

Explanation:

Step1: Apply Pythagorean theorem

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

Step2: Calculate \(12^{2}+5^{2}\)

\(12^{2}=144\), \(5^{2} = 25\). Then \(x^{2}=144 + 25\).
\(x^{2}=169\).

Step3: Solve for \(x\)

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

Answer:

\(13\)