Question

In a Δ ABC, D and E are points on the sides AB and AC respectively such that DE || BC. If AD = 2.5 cm, BD = 3.0 cm, and AE = 3.75 cm, find the length of AC.

Answer 1

Given: AD = 2.5 cm, AE = 3.75 cm and BD = 3 cm 

Required to find AC. 

By using Thales Theorem, [As DE ∥ BC] 

\(\frac{AD}{BD} = \frac{AE}{CE}\) 

\(\frac{2.5}{3} = \frac{3.75}{CE}\) 

2.5 x CE = 3.75 x 3 

CE = \(\frac{3.75 \times 3}{2.5}\) 

CE = \(\frac{11.25}{2.5}\)

CE = 4.5 

Now, AC = 3.75 + 4.5 

∴ AC = 8.25 cm.