Question

find the value of x in the triangle shown below.

Explanation:

Step1: Apply Pythagorean theorem

For a right - triangle with legs \(a\) and \(b\) and hypotenuse \(c\), the formula is \(a^{2}+b^{2}=c^{2}\). Here \(a = 2\), \(b = 8\), and \(c=x\). So \(2^{2}+8^{2}=x^{2}\).

Step2: Calculate the squares

\(2^{2}=4\) and \(8^{2}=64\), then \(4 + 64=x^{2}\), so \(x^{2}=68\).

Step3: Solve for \(x\)

Take the square root of both sides. Since \(x\) represents the length of a side of a triangle, we take the positive square root. \(x=\sqrt{68}=\sqrt{4\times17}=2\sqrt{17}\).

Answer:

\(2\sqrt{17}\)