Question

∆ ABC and ∆ DEF are equilateral triangles A( ABC): A(∆DEF=1:2 if AB =4 then what is the length of DE​

Answer 1

Answer:

Given: ∆ABC and ∆DEF are equilateral triangles

Constrcution: Draw a perependicular from vertex A and D on AC and DF in both triangles.

In ∆ABX and ∆DEY

∠B = ∠C = 60∘ (∆ABC and ∆DEF are equilateral triangles)

∠AXB = ∠DYB (By construction)

By AA test of similarity

1. ∆ABX ~ ∆DEY