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in Geometry by (15.8k points)
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In ΔDEF, DN, EO, FM are medians and point P is the centroid. Find the following.

(i) If DE = 44, then DM = ?

(ii) If PD = 12, then PN = ?

(iii) If DO = 8, then FD = ?

(iv) If OE = 36, then EP = ?

1 Answer

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Best answer

Given DN, EO, FM are medians.

∴ FN = EN

DO = FO

EM = DM

(i) If DE = 44, then

DM = 44/2 = 22

DM = 22

(ii) If PD = 12, PN = ?

PD/PN = 2/1

12/PN = 2/1 ⇒ PN = 12/2 = 6

PN = 6

(iii) If DO = 8, then

FD = DO + OF = 8 + 8

FD = 16

(iv) If OE = 36,

then EP/PO = 2/1

EP/2 = PO

OE = OP + PE

36 = PE/2 + PE

36 = PE/2 + 2PE/2

36 = 3PE/2

PE = (36×2)/3

PE = 24

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