mathspassion Posted December 24, 2016 Posted December 24, 2016 In a Right angle triangle ABC AB=3,AC=4 & BC=5 at BC,E is middle point and D is altitude AD Find distance DE=? it is not a difficult question eveyone who know maths can solve easly but question is solve it in one line...........
Sriman Dutta Posted December 24, 2016 Posted December 24, 2016 (edited) [math] DE=BE-BD=\frac{BC}{2} -\sqrt{AB^2-AD^2}=\frac{BC}{2}-\sqrt{AB^2-(\frac{AC.AB}{BC})^2}[/math] Edited December 24, 2016 by Sriman Dutta
imatfaal Posted December 25, 2016 Posted December 25, 2016 Not sure if this is short enough for you As triangles ABC and ADC are similar in a ratio of 5:4, DC is 4/5 of AC, EC is by definition 1/2 of BC; thus DE is (4/5)*4-(1/2)*5= 0.7 2
mathspassion Posted December 26, 2016 Author Posted December 26, 2016 is it for 345 only or for 5 12 13 as well..... my mean is to everyone can solve it (it is still too lengthy) , it can be too short if you know there is a new formula recently obtained. study deep
imatfaal Posted December 26, 2016 Posted December 26, 2016 Between intersection of altitude and bisector on hypotenuse BC of any right-triangle ABC is (AC x AC/BC) - BC/2 where AC is longer leg That's one line and general - dunno what new formula you might be referring. Perhaps you could stop being so elliptic and ask in a more straight forward manner
michel123456 Posted December 26, 2016 Posted December 26, 2016 In a Right angle triangle ABC AB=3,AC=4 & BC=5 at BC,E is middle point and D is altitude AD Find distance DE=? it is not a difficult question eveyone who know maths can solve easly but question is solve it in one line........... If I follow your setup D is in the middle of AB, then the distance DE is half AC=2
imatfaal Posted December 26, 2016 Posted December 26, 2016 If I follow your setup D is in the middle of AB, then the distance DE is half AC=2 The altitude of a triangle divides the angle and forms a perpendicular to the side opposite the angle; ie D must lie on BC (side opposite A) and line AD must be perpendicular to line BC * * I think for the other two side/angles of a right triangle the altitude is the same as the side itself - but for the hypoteneuse / right angle this is not the case
michel123456 Posted December 27, 2016 Posted December 27, 2016 (edited) The altitude of a triangle divides the angle and forms a perpendicular to the side opposite the angle; ie D must lie on BC (side opposite A) and line AD must be perpendicular to line BC * * I think for the other two side/angles of a right triangle the altitude is the same as the side itself - but for the hypoteneuse / right angle this is not the case Thank you. I missed a sketch.. And now that I put it on paper I realize your post #3 is correct. +1 Edited December 27, 2016 by michel123456
michel123456 Posted December 29, 2016 Posted December 29, 2016 (edited) I couldn't post images the other day. Edited December 29, 2016 by michel123456 1
mathspassion Posted January 2, 2017 Author Posted January 2, 2017 sir figure is right AB=3,AC=4 AND BC=5 as per figure find DE=? only two seconds question if you know the particular theorum which recently obtained by .....................
mathspassion Posted April 12, 2017 Author Posted April 12, 2017 (edited) bare links removed by moderator Edited April 12, 2017 by imatfaal removal of links
imatfaal Posted April 12, 2017 Posted April 12, 2017 ! Moderator Note ...Links, pictures and videos in posts should be relevant to the discussion, and members should be able to participate in the discussion without clicking any links or watching any videos.... Scienceforums.net rules. Please do not post bare links - I have removed those links as members have no guarantee of the content/safety.
Commander Posted April 12, 2017 Posted April 12, 2017 sir figure is right AB=3,AC=4 AND BC=5 as per figure find DE=? only two seconds question if you know the particular theorum which recently obtained by ..................... I get DE = [ AC2 - AB2 ] / 2 x BC as a General Solution and therefore [42 - 32 ] /2 x5 = 7/10 = 0.7 in this case [the same result found by imatfaal !
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