Answer: AD = x√3
AD² = 3x²
Step-by-step explanation:
If ΔABC is equilateral and is cut by a perpendicular, then the resulting two triangles (ΔBDA & ΔBDC) are both 30°-60°-90° triangles where
∠A = 30°
∠D = 90°
∠B = ∠C = 60°
In a 30° - 60° - 90° triangle, the corresponding sides have lengths of
↓ ↓ ↓
b b√3 2b
Thus: BD = CD = b
AD = b√3
AB = AC = 2b
Since it is given that AB = 2x, replace the "b" above" with an "x"
BD = x, CD = x
AD = x√3
AB = 2x, AC = 2x
I'm not sure what the statements are because they are squished together but hopefully the information I provided will allow you to finish answering the question.
