Question

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

Explanation:

Step1: Find the base of the rectangle

The bottom side of the rectangle is equal to the hypotenuse of the right triangle with legs 5 and 9. Using the Pythagorean theorem \( c = \sqrt{a^2 + b^2} \), where \( a = 5 \) and \( b = 9 \).

$$ c = \sqrt{5^2 + 9^2} = \sqrt{25 + 81} = \sqrt{106} $$

Step2: Find the length of the dotted line

The dotted line is the diagonal of the rectangle with height 7 and base \( \sqrt{106} \). Using the Pythagorean theorem again, let \( d \) be the diagonal.

$$ d = \sqrt{7^2 + (\sqrt{106})^2} = \sqrt{49 + 106} = \sqrt{155} \approx 12.4 $$

Answer:

\( 12.4 \)