Question

1. find the missing side length. show all work to explain your reasoning.

12
x
5

Explanation:

Step1: Apply Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), where \(a = 5\), \(b=12\), and \(c=x\).

Step2: Substitute values into the formula

Substitute \(a = 5\) and \(b = 12\) into \(a^{2}+b^{2}=c^{2}\), we get \(5^{2}+12^{2}=x^{2}\).
Calculate \(5^{2}=25\) and \(12^{2}=144\). Then \(25 + 144=x^{2}\), so \(x^{2}=169\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x>0\) (length of a side), \(x=\sqrt{169}\).

Answer:

\(x = 13\)