In an equilateral triangle PQR, if p, q and r denote the lengths perpendiculars from P, Q, R respectively on the opposite sides, then
p = q = r
p ≠ q = r
p = q ≠ r
If PQR is an equilateral triangle then the length of the perpendiculars dropped from points P, Q and R are also equal.
Hence, p=q=r