In ∆ABC, point D is the centroid. If (AE) ̅=15, (BF) ̅=27, and (CD) ̅=8, find the following lengths

Mathematics

1 answer:

Anna71 [15]2 years ago

7 0

Answer:

5,18,12 cms are the answer.

Step-by-step explanation:

Given is a triangle ABC. Point D is the centroid.

E,F and G are midpoints of CB, BA and AC respectively.

AE, BF and CG are medians of the triangle.

We know that centroid divides the median in the ratio 2:1

Using this we find that AD:DE = 2:1

Or AD+DE:DE = (2+1):1

AE:DE =3:1

15:DE = 3:1 . Hence DE =5 cm.

On the similar grounds we find that DF = 1/3 BF = 9

Hence BD = DF-BF = 27-9 =18 cm

and also

CG = 3/2 times CD = 12 cm.

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