Question

what is the value of x?
\\( \frac { 1 } { 3 } \sqrt { 2 } \\) units
\\( \frac { 1 } { 2 } \sqrt { 3 } \\) units
\\( 2 \sqrt { 3 } \\) units
\\( 3 \sqrt { 2 } \\) units

Explanation:

Step1: Use Pythagorean theorem for the large right - angled triangle

The Pythagorean theorem states that in a right - angled triangle \(a^{2}+b^{2}=c^{2}\), where \(a\) and \(b\) are the legs and \(c\) is the hypotenuse. Here, \(a = 3\), \(b=3\), and \(c\) is the hypotenuse of the large right - angled triangle.

$$c=\sqrt{3^{2}+3^{2}}=\sqrt{9 + 9}=\sqrt{18}=3\sqrt{2}$$

Since \(x\) is the hypotenuse of the large right - angled triangle, \(x = 3\sqrt{2}\) units.

Answer:

\(3\sqrt{2}\) units