P, Q and R are the mid points of XO, YO and ZO respectively as shown in figure. If PQ = 4 cm, QR = 6 cm and PR = 8 cm, then find the lengths of the sides of ΔXYZ.

Answer : 
Given P , Q and R are the mid points on  XO , YO and ZO. 
And 
PQ = 4 cm
QR = 6 cm
PR = 8 cm
P, Q and R and XO, YO and ZO are arrange in figure like:

In $∆$ZXO
PR is the mid segment as it connects the mid points of two sides XO and ZO, Then we know the mid segment is always half the length of the third side in triangle.
SO 
PR = $\frac{1}{2}$ XZ
$\Rightarrow$XZ = 2 ( PR ) 
$\Rightarrow$XZ = 16    cm          ( Given PR = 8 cm)

Similarly In​ $∆$YZO
QR is the mid segment as it connects the mid points of two sides YO and ZO, Then we know the mid segment is always half the length of the third side in triangle.
SO 
QR = $\frac{1}{2}$ YZ
$\Rightarrow$YZ = 2 ( QR ) 
$\Rightarrow$YZ = 12    cm          ( Given QR = 6 cm)

And,

In $∆$XYO
PQ is the mid segment as it connects the mid points of two sides XO and YO , Then we know the mid segment is always half the length of the third side in triangle.
SO 
PQ = $\frac{1}{2}$ XY
$\Rightarrow$XY = 2 ( PQ ) 
$\Rightarrow$XY = 8    cm          ( Given PQ = 4 cm)

SO sides of triangle XYZ are as XY = 8 cm , YZ = 12 cm  And ZX = 16 cm           (Ans)