Question

find the length of the third side. if necessary, round to the nearest tenth. answer attempt 1 out of 2

Explanation:

Step1: Identify the triangle type

It's a right - triangle. Let the sides be \(a = 2\), \(b\) (unknown), and \(c = 4\). Assume \(c\) is the hypotenuse.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is \(a^{2}+b^{2}=c^{2}\), so \(b=\sqrt{c^{2}-a^{2}}\).
Substitute \(a = 2\) and \(c = 4\) into the formula: \(b=\sqrt{4^{2}-2^{2}}=\sqrt{16 - 4}=\sqrt{12}\).

Step3: Simplify and round

\(\sqrt{12}\approx3.5\)

Answer:

3.5