Instructions: DO NOT USE CALCULATOR. Figures are not drawn to scale. In the figure, AD is parallel to BC. BC = 12 cm and AD = 3 cm. If AE = 2 cm, what is the length of EC in cm?
Explanation: (B) Since AD is parallel to BC, the triangles \(\triangle ADE\) and \(\triangle CBE\) are similar. The ratio of corresponding sides is equal: \(\frac{AD}{BC} = \frac{AE}{EC}\). \(\frac{3}{12} = \frac{2}{EC}\). Cross-multiplying: \(3 \cdot EC = 12 \cdot 2 \implies 3 \cdot EC = 24 \implies EC = 8 \text{ cm}\).
