In the figure below, $ABEF$ is a rectangle, $\overline{AD} \perp \overline{DE}$, $AF=7$, $AB=1$, and $AD=5$.
$\textbf{(A) } \frac{3}{8} \qquad\textbf{(B) } \frac{4}{9} \qquad\textbf{(C) } \frac{1}{8}\sqrt{13} \qquad\textbf{(D) } \frac{7}{15} \qquad\textbf{(E) } \frac{1}{8}\sqrt{15}$
Difficulty:
40/100 — On the trickier side; hard to compute if similarity is not realized.
Core Concepts:
similarity, right triangle
Challenges:
May seem unreasonably computation-heavy for beginners; hard to approach creatively.
Techniques:
Utilize properties of similar triangles for an algebraic context (Pythagorean theorem.)
Error-prone Steps:
Incorrectly simplifying the equation received from similar triangles.
Ideal Time:
Experienced: ≤ 1-2 min
Intermediate: ≤ 2 min
Beginner: ≤ 4-5 min
