Question

Consider that △ABC is an equilateral triangle, and AD is a perpendicular bisector of △ABC.

Equilateral triangle A B C is cut by perpendicular bisector A D.

If AB = 2x, complete the statements below.


2 + (AD)2 = (2x)2
(AD)2 =
x2 – x2
(AD)2 =
x2
AD =

Answer 1

In right triangle ABD (D midpoint of BC), AB^2 = AD^2 + BD^2. Since AB = 2x and BD = 1/2 AB = x:

(AD)^2 = (2x)^2 − x^2 = 4x^2 − x^2 = 3x^2

Thus AD = √(3x^2) = x√3.