In a triangle ABC, D and E are points on AB and AC respectively such that DE ∥ BC. if AD = 2.4cm, AE=3.2cm, DE=2cm and BC=5cm, find BD and CE

Question

I'm aware that the required values can be found using the concept of similarity of triangles ($ADE$ and $ABC$) but another requirement is that the question should be solved without using the concept of similarity in any step of the solution. Kindly assist me in finding the required values $BD$ and $CE$. This is a really urgent question. Thank you

Answer 1

$$\frac{AC}{3.2}=\frac{AB}{2.4}=\frac{5}{2}$$Cross-multiplying,$$AC=\frac{5}{2}\cdot 3.2=8$$and$$AB=\frac{5}{2}\cdot 2.4=6$$So$$EC=AC-AE=8-3.2=4.8$$and$$DB=AB-AD=6-2.4=3.6$$But the first proportion above follows from similar triangles. Does the Intercept Theorem rest on an independent foundation?