In triangle ABC, AB = 10 and AC = 17. Let D be the foot of the perpendicular from A to BC. If BD:CD = 3:5, then find AD.
a2 + b2 = c2
a2 + b2 = 102
a2 + b2 = 172
Using the info that it is a 3:5 ratio, you can determine that the maximium numbers it can be is 6:10 without being 10.
All other 3:5 ratios under 10 not using decimals are 3:5, since that would give AD = 16.7 and 8.6 which don't match up, so it isn't a whole number.
Next I used a simultaneus equation: 289 - y = 100 - x and 3y = 5x.
What I got was x = 567/2 or 283.5 and y = 945/2 or 472.5
Squaring them gave me the answer: x = 16.8 and y = 21.7 which still didn't make sense.
So then I thought about it and it's impossible.
The question as written leads to a complex value for AD!!!! Hoever, if BD/CD = 2:5 then AD has a more sensible value (=8).
If the ratio of BD:CD = 2 : 5 then 102 - (2x)2 = 172 - (5x)2
x = 3 side BC = 21
In case of 3 : 5 ratio, we have: 102 - (3x)2 = 172 - (5x)2
x = 3.43693
BC = 27.49544 Impossible!