Question

solve for x to the nearest tenth.

Explanation:

Step1: Find the length of the hypotenuse of the small right - triangle

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for the small right - triangle with \(a = 2\) and \(b = 4\).
\[c_{1}=\sqrt{2^{2}+4^{2}}=\sqrt{4 + 16}=\sqrt{20}=2\sqrt{5}\]

Step2: Find the length of the hypotenuse of the large right - triangle

The two right - triangles are combined, and the vertical side of the large right - triangle is \(2 + 10=12\) and the horizontal side is \(4\).
The length of the hypotenuse \(x\) of the large right - triangle can be found using the Pythagorean theorem \(x=\sqrt{(2 + 10)^{2}+4^{2}}\).
\[x=\sqrt{12^{2}+4^{2}}=\sqrt{144 + 16}=\sqrt{160}=4\sqrt{10}\approx 4\times3.162 = 12.648\approx12.6\]

Answer:

\(12.6\)