Question

find the value of the variable(s). if your answer is not an integer, leave it in simplest radical form.
7
multiple choice 1 point
not drawn to scale
\frac{1}{2}
7\sqrt{3}
2
14\sqrt{3}

Explanation:

Step1: Use Pythagorean theorem

In a right - triangle, if one side is \(a = 7\), hypotenuse \(c = 14\), and the other side is \(x\). By Pythagorean theorem \(a^{2}+x^{2}=c^{2}\).

Step2: Substitute values

Substitute \(a = 7\) and \(c = 14\) into \(a^{2}+x^{2}=c^{2}\), we get \(7^{2}+x^{2}=14^{2}\).

$$
LATEXBLOCK0
$$

Step3: Simplify the radical

Factor \(147=49\times3\), then \(x=\sqrt{147}=\sqrt{49\times3}\).
Since \(\sqrt{ab}=\sqrt{a}\cdot\sqrt{b}(a\geq0,b\geq0)\), so \(x = 7\sqrt{3}\).

Answer:

\(7\sqrt{3}\)