2023 AMC 8 Problems/Problem 24

Revision as of 20:46, 24 January 2023 by Pi is 3.14 (talk | contribs) (Video Explanation (along with thought process) Using Lots of Similarity)

Problem

Isosceles $\triangle ABC$ has equal side lengths $AB$ and $BC$. In the figure below, segments are drawn parallel to $\overline{AC}$ so that the shaded portions of $\triangle ABC$ have the same area. The heights of the two unshaded portions are 11 and 5 units, respectively. What is the height of $h$ of $\triangle ABC$?

  • Add asymptote diagram*

(note: diagrams are not necessarily draw to scale)

\[\textbf{(A) } 14.6 \qquad \textbf{(B) } 14.8 \qquad \textbf{(C) } 15 \qquad \textbf{(D) } 15.2 \qquad \textbf{(E) } ~15.4\]

Video Solution 1 by OmegaLearn (Using Similarity)

https://youtu.be/almtw4n-92A