Question

find the length of the third side. if necessary, round to the nearest tenth.

Explanation:

Step1: Identify the formula

Use the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\) for a right - triangle, where \(c\) is the hypotenuse. Here, if we assume the two given sides are \(a = 2\) and \(b\) is the unknown side, and \(c = 4\). Then \(b=\sqrt{c^{2}-a^{2}}\).

Step2: Substitute the values

We have \(a = 2\) and \(c = 4\). Substitute into the formula \(b=\sqrt{4^{2}-2^{2}}=\sqrt{16 - 4}=\sqrt{12}\).

Step3: Simplify and round

\(\sqrt{12}\approx3.5\) (rounded to the nearest tenth).

Answer:

3.5