Question

consider that △abc is an equilateral triangle, and ad is a perpendicular bisector of △abc. if ab = 2x, complete the statements below. x²+(ad)²=(2x)² (ad)²= (ad)²=2x² - x² ad = √3

Explanation:

Step1: In equilateral △ABC, BD = DC = x.

In right - triangle ABD, by Pythagorean theorem \(AB^{2}=BD^{2}+AD^{2}\).

Step2: Substitute AB = 2x and BD = x.

\((2x)^{2}=x^{2}+(AD)^{2}\), so \((AD)^{2}=(2x)^{2}-x^{2}=3x^{2}\), then \(AD = \sqrt{3}x\).

Answer:

\((AD)^{2}=(2x)^{2}-x^{2}\), \(AD=\sqrt{3}x\)