SOLUTION: The triangle A (lower left hand corner of the triangle) B (lower right hand corner) C (top of triangle) =ABC, is an equilateral triangle where each side of the triangle is 6. What

Question 26340: The triangle A (lower left hand corner of the triangle) B (lower right hand corner) C (top of triangle) =ABC, is an equilateral triangle where each side of the triangle is 6. What is the height of h if h is the dotted vertical line down the center?
I am having a hard time trying to copy and paste the triangle with my question. Hopefully, you can imagine what I am trying to say. The picture looks like an equilateral triangle w/ a dotted vertical line down the middle. The three sides of the triangle is 6 and the three points of the triangle is ABC.
Thanks,
Kristin
Answer by venugopalramana(3286) (Show Source): You can put this solution on YOUR website!
LET ABC BE THE TRIANGLE. AND LET AD BE THE HEIGHT SHOWN BY A PERPENDICULAR FRO A TO BC.D IS ON BC. IN TRIANGLES ABD AND ACD WE HAVE
AB=AC=6
AD=AD
ANGLE ADB = 90 = ANGLE ADC
HENCE THE 2 TRIANGLES ARE IDENTICAL HENCE BD = DC
BUT BC=BD+DC=6 ...SO BD=DC=3
IN RIGHT ANGLED TRIANGLE ABD WE HAVE ,ANGLE ADB =90 DEGREES
HYPOTENUSE = AB =6
BD =3
SO
AD^2+BD^2=AB^2
AD^2+3^2=6^2
AD^2=36-9=27
AD=SQ.RT.27 = 3*SQRT3
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