Given right triangle A, B, CABC with altitude start overline, B, D, end overline
BD
drawn to hypotenuse start overline, A, C, end overline
AC
. If B, D, equals, 33BD=33 and D, C, equals, 11, commaDC=11, what is the length of start overline, A, D, end overline, question mark
AD
?
To find the length of AD, we will use the concept of similar triangles.
In triangle ABD, BD is the altitude drawn to the hypotenuse AC. This splits the right triangle into two smaller similar triangles: ABD and BDC.
Since the triangles ABD and BDC are similar, we can set up the following proportion:
AD/BD = BD/DC
Substitute the given values:
AD/33 = 33/11
AD = 33*33/11
AD = 99
Therefore, the length of AD is 99.