geometry
posted by Jacqueline .
In the diagram below, the length of the legs AC and BC of right triangle ABC are 6cm and 8cm, respectively.Altitude CD is drawm to the hypotenuse of triangle ABC.
what is the lenght of AD to the nearest tenth of a centimeter?

3,4,5 right trisangle so
hypotenuse = 10
Draw it and note similar triangles ABC, CBD, ACD
call AD = x
then BD = 10x
the altitude CD = sqrt (36x^2)
the altitude CD = sqrt (64 (10x)^2)
so
36x^2 = 64  (10x)^2
36  x^2 = 64  ( 100 20 x + x^2)
36  x^2 = 36 + 20 x  x^2
72 = 20 x
x = 72/20 = 3.6 
ur mom