SOLUTION: BD is the altitude of right triangle ABC. If AD=3 and DC=12, what is the length of BD?

Algebra ->  Pythagorean-theorem -> SOLUTION: BD is the altitude of right triangle ABC. If AD=3 and DC=12, what is the length of BD?       Log On


   

Question 1140950: BD is the altitude of right triangle ABC. If AD=3 and DC=12, what is the length of BD?

Found 2 solutions by josmiceli, MathLover1:
Answer by josmiceli(19441) About Me  (Show Source):
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
BD is the altitude of right triangle ABC.
If AD=3+and DC=12, what is the length of BD?




given: right triangle ABC=> angle B+=+90° and altitude divides angle B into two angles , < 1 and < 2+
=> <1+%2B+2+=+90° ……(1)
BD is perpendicular to+AC+( given)
=> <1 + < DCB+=+90° …….(2)
=> < DCB+= < 2 ………….by (1) & (2)
& < BAD = <1
So, triangle+BCD ~ triangle+ABD ( by AAA similarity theorem)
=> BC%2FAB+=+CD%2FBD+=+BD%2FAD ( corresponding sides of similar triangles)
=> BC%2FAB+=+12%2FBD+=+BD%2F3
= BD%5E2+=+36
=> BD+=+sqrt%2836%29
=> BD+=+6