In triangle ABC with centroid H, given BG = 57 and CD = 34, the line segments are BH = 38, HF = 19, GD = HG = 17, CH = 56.67, and ED = 45.33.
To determine the lengths of line segments in triangle ABC, given that H is the centroid and BG = 57 and CD = 34, we follow these steps:
1. BH (Base of the Triangle): Since H is the centroid, BH is 2/3 of BG. Therefore, BH = 2/3 * 57 = 38.
2. HF (Height from H to Base): HF is 1/3 of BG. So, HF = 1/3 * 57 = 19.
3. GD (Altitude from G to Base): GD is equal to HG and is 1/2 of CD. Thus, GD = HG = 1/2 * 34 = 17.
4. CH (Altitude from C to Base): CH is 5/3 of CD. Hence, CH = 5/3 * 34 = 56.67.
5. ED (Altitude from E to Base): ED is 4/3 of CD. Consequently,
ED = 4/3 * 34 = 45.33.
In summary, the line segment lengths are: BH = 38, HF = 19, GD = 17, HG = 17, CH = 56.67, and ED = 45.33.
Que. give the diagram below if H is the centroid of BCD, BG=57, CD=34, EH=15 and CF=39. find the length of GD, BH, HF, HG, CH, ED