In an equilateral triangle of side 3 square root of 3cm, find the length of the altitude.

Asked by Jerlin George | 21st Sep, 2015, 10:15: AM

Expert Answer:

 
 
 
begin mathsize 14px style Let space the space given space equilateral space triangle space be space ABC space Given colon space length space of space the space sides space equals space 3 √ 3 The space altitude space divides space the space equilateral space triangle space into space two space equal space right space angled space triangles. The space base space of space space triangle space ABC space gets space divided space into space two space equal space parts.  Let space straight x space be space the space length space of space the space altitude. Consider space increment ABD Length space of space base space AD space equals 3 √ 3 divided by 2 space equals space fraction numerator space 3 √ 3 over denominator 2 end fraction space space The space sides space of space straight a space right space angled space triangle space ABD space satisfy space Pythagoras ’ space rule therefore open parentheses space 3 √ 3 close parentheses squared space equals space straight x squared space plus space open parentheses fraction numerator space 3 √ 3 over denominator 2 end fraction close parentheses squared therefore 27 space equals space straight x squared space plus space 27 over 4 therefore straight x squared space equals space 27 minus 27 over 4 therefore straight x squared space equals space fraction numerator 108 minus 27 over denominator 4 end fraction equals 81 over 4 therefore straight x equals square root of 81 over 4 end root equals 9 over 2 Therefore space length space of space altitude space equals space 4.5 space cm end style

Answered by Priti Shah | 21st Sep, 2015, 09:12: PM

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