Question 482448
c is the midpoint of ab, d is the midpoint of ac, e is the midpoint of ad, f is the midpoint of ed, g is the midpoint of ef, and h is the midpoint of db. if dc is =16 find gh.


It’s given that DC = 16, but since we know that DC = ¼AB (½ of ½AB), we can say that: ¼AB = 16. This means that AB = 64. 

GF = {{{(1/32)AB}}}, or {{{(1/32)64}}}, or 2, and FD = {{{(1/16)AB, or {{{1/16)64}}}, or 4. Also, we can see that AD = ¼(AB), or ¼(64), or 16. 


Now, since AB = 64, and AD = 16, then DB must = 48 (64 – 16). And, since it was given that H is the midpoint of DB, it follows that DH = HB = ½DB, or ½(48), or 24. 


Since GH = GF + FD + DH, then GH = 2 + 4 + 24 = {{{highlight_green(30)}}}.