In Delta MNP medians MB NA and PC intersect at centroid Q If

In Delta MNP, medians MB, NA, and PC intersect at centroid Q. If MQ = 8, find QB If QC = 3, find PQ. If AQ = 3.5, find AN. If MP = 10, find MA.

Solution

We know that

The centroid of a triangle divides each median in the ratio 2:1

Hence ,

MQ:QB = NQ:QA = PQ:QC = 2:1

a ) Given that

MQ = 8

QB = 2MQ

QB = 2(8)

QB = 16

b ) QC = 3

QC = 2PQ

3 = 2PQ

3/2 = PQ

PQ = 3/2

c ) AQ = 3.5

AQ = 2NA

3.5 = 2NA

(3.5)/2 = NA

NA = (3.5)/2

NA = 1.75

d ) MP = 10

We know that

The meadian divides the side in equal ratio

Hence ,

MP = MA + AP

10 = 5 + 5

Therefore ,

MA = 5