In a triangular park ABC a walking track runs from a point D on the boundary AB to a point E on the boundary AC, parallel to BC. The planner wants the track placed so that it cuts off exactly one quarter of AB measured from the corner A. If AC is 96 m long, how far from A along AC should E be fixed (in m)?

Question

Accepted Answer

24. "One quarter of AB from A" means AD/AB = 1/4. Since DE is parallel to BC, AE/AC = AD/AB = 1/4, so AE = 1/4 × 96 = 24 m. The value 32 comes from turning 1/4 into AD : DB = 1 : 3 and then taking 1/3 of 96 — mixing a part-to-part ratio into a part-to-whole calculation; 72 is EC; 48 halves AC.

Step-by-Step Solution

Master this chapter in 30 minutes a day.

More Class 10 Basic Proportionality Theorem practice