Question

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

Explanation:

Step1: Identify right - angled triangle

The dotted line is the hypotenuse of a right - angled triangle with legs \(a = 10\) and \(b=7 + 5=12\).

Step2: Apply Pythagorean theorem

The Pythagorean theorem is \(c=\sqrt{a^{2}+b^{2}}\), where \(c\) is the hypotenuse and \(a\) and \(b\) are the legs. Substitute \(a = 10\) and \(b = 12\) into the formula: \(c=\sqrt{10^{2}+12^{2}}=\sqrt{100 + 144}=\sqrt{244}\).

Step3: Calculate and round

\(\sqrt{244}\approx15.6\).

Answer:

15.6