Question

If triangle xyz, G is centroid. if xy = 11,yz=14 and xz=7 cm, Then what is the value of Gm ,
m point upon yz ​

Answer 1

The value of GM is 2 cm.

According to Apollonius Theorem,  

(XY)* (XY)+ (XZ)*(XZ) =2*[7*7+ (XM)*(XM)]

So, According to the image attached,

11*11 + 7*7=2*[7*7+ (XM)*(XM)]

So, (XM)*(XM) = ½ [(11*11)-(7*7)]

So, (XM)*(XM)  = 36

So, XM=6

As per the question, G is the centroid. It will divide the altitude XM in 2: 1 ratio as shown in figure.

So, GM=1/3 XM

So, GM= 1/3 *6 cm

So, GM = 2 cm