Everyday Triangle Problem

Geometry Level 4

A triangle Δ A B C \Delta ABC has side lengths of 5 5 , 7 7 and 9 9 units respectively.

A D ⊥ B C AD \perp BC is drawn. Similarly, B E ⊥ A C BE \perp AC is drawn.

Find the length of D E DE to 2 decimal places.

Note: The image given is just for reference and not to be scaled. The actual figure may vary.


The answer is 4.166.

Avineil Jain by Avineil Jain , 24, Netherlands

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2 solutions

Anway Deshpande
Jun 6, 2014

Apply cosine rule to get cosC and as DE is a side of the orthic configuration DE=c*cosC

1 Helpful 0 Interesting 0 Brilliant 0 Confused
Filly Mare
Jul 28, 2014

I used cosine rule to find angle C, then found the length of AD and DC and hence BD. Applied the coordinates (0,0) to point B and then worked out the coordinates of A, D and C from that. Then calculated gradient of AC, perpendicular gradient (BE). Found equations of lines AC and BE and then the intersection point (E) Then distance formula for DE.

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