what is the length of the dotted line in the diagram below? round to the nearest tenth.

Explanation:

Step1: Identify the right - triangle

The dotted line is the hypotenuse of a right - triangle with legs of lengths 7 and 10.

Step2: Apply the Pythagorean theorem

The Pythagorean theorem is (c=\sqrt{a^{2}+b^{2}}), where (a = 7) and (b = 10). So (c=\sqrt{7^{2}+10^{2}}=\sqrt{49 + 100}=\sqrt{149}).

Step3: Calculate the value and round

(\sqrt{149}\approx12.2).

Answer:

12.2