Question

what is the length of the dotted line in the diagram below? round to the nearest tenth. 10 6 8 answer attempt 1 out of 3 submit answer

Explanation:

Step1: Find the base of the rectangle

The triangle at the bottom is a right triangle with legs 6 and 8. Using the Pythagorean theorem \(a^2 + b^2 = c^2\) (where \(a = 6\), \(b = 8\)) to find the hypotenuse (which is the base of the rectangle).
\(c = \sqrt{6^2 + 8^2} = \sqrt{36 + 64} = \sqrt{100} = 10\)

Step2: Find the length of the dotted line

The dotted line is the diagonal of a rectangle with length 10 (from step 1) and height 10. Using the Pythagorean theorem again, where \(a = 10\), \(b = 10\).
\(d = \sqrt{10^2 + 10^2} = \sqrt{100 + 100} = \sqrt{200} \approx 14.1\)

Answer:

14.1