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 = 16, find GH
2007-08-27 11:14:21 · 9 answers · asked by iluvcaliii06 2 in Science & Mathematics ➔ Mathematics
Draw a line; label the ends A and B. Put all the letters in the right place; note that DC is 1/4 the length of the original line (halfway between halfway). So the whole line AB is 64.
Each letter divides the previous letters in half; by the time you get to H, you are at 1/64 units, so GH is 1.
2007-08-27 11:22:09 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Draw the line as stated. DC is 1/4 of the total length, FG is 1/32, FD is 1/16. You will find that H is 5/8 of the way from A to B, so...
GH = 1/32 + 1/16 + 1/4 + 1/8 of the total length. You also know that DC = 1/4 = 16, so...
(1/8)*16 + (1/4)*16 + 16 + (1/2)*16 = 30.
2007-08-27 11:26:35 · answer #2 · answered by Mathsorcerer 7 · 0⤊ 0⤋
I did this in terms of fractios of AB.
AC=CB=1/2 AB
AD=DC=1/4 AB
AE=ED= 1/8 AB
EF=FD=1/16 AB
EG=GF=1/32 AB
Now comes the difficult part, figuring out what DH=HB is.
You can figure out from the stuff above that DB=3/4 AB, so half of that is 3/8 AB. AD=1/4 AB, so AH=AD+DH= 5/8 AB
Now it shouldn't be too bad.
AH=5/8 AB, and AH = AE + EG + GH
We know all of those except for GH, so plug in and solve for GH in terms of AB.
5/8 AB = 1/8 AB + 1/32 AB + GH
So GH = (5/8 - 1/8 - 1/32) AB
GH = 15/32 AB
We know DC=16 and DC=1/4 AB, so AB=64
Plug that into the expression for GH, and we get GH=30.
2007-08-27 11:32:39 · answer #3 · answered by J2S 2 · 0⤊ 0⤋
GH =30
If DC=16, and D is the midpoint of AD, AC=32, so BC also equals 32.
If BC=32 and DC=16, BD=48. H is the midpoint, so BH=24.
BC=32 and BH=24, so HC=8.
Working on the other half of the line, AE is half of AD, so AE=8.
FD is half of DE, so FD=4. GF is half of FD, so GF=2.
GF+FD+DC+CH=GH => 2+4+16+8=30.
Here's a rough approximation of the line:
A....E.G.F..D........C....H............
B
2007-08-27 11:41:55 · answer #4 · answered by cmh0114 3 · 0⤊ 0⤋
Damn. I am so good at Geo. I passed w/ a 86% last year. But... the way u wrote it makes it all confuseing. Try re-writing it.
Kindra
2007-08-27 11:19:10 · answer #5 · answered by Anonymous · 0⤊ 0⤋
30.
2007-08-27 11:25:45 · answer #6 · answered by Eric C 2 · 0⤊ 0⤋
hmm..
cant draw perfectly but here goes..
A----E-G-F--D----C----H------------B
given
DC = 16
AC = CB
SO:
DC = 16
AD = 16
AE = 8
ED = 8
EF = 4
EG = 2
GD = 6-
FD = 4
DC = 16-
CH = 8-
SO ADDING EG,DC, AND CH = 16+6+8 = 30
the length of GH = 30
2007-08-27 11:30:41 · answer #7 · answered by toffer 3 · 0⤊ 0⤋
Angle B = 80 Angle C = 80
2016-05-19 04:30:26 · answer #8 · answered by dorene 3 · 0⤊ 0⤋
30.64
2007-08-27 11:28:40 · answer #9 · answered by Beth S 2 · 0⤊ 0⤋