Question

triangle ABC and triangle PQR are equilateral triangles ,A{△ABC}:A{△PQR}=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

∆ABX ~ ∆DEY