Answer: NP= 16 cm
Explanation:
As we shown in the figure below :
Since P is the midpoint of MN and NQ
So, We consider ΔMNP and ΔPQR,
∠MPN=∠QPR (∵ Vertically opposite angles are equal)
MP=PR (∵ P is the mid point of MR)
NP=PQ (∵P is the midpoint of NQ)
So, ΔMNQ ≅ ΔPQR (∵By SAS congruence )
∴ [tex]26=6x+2 \text{(By CPCT )}\\26-2=6x\\24=6x\\\frac{24}{6}=x\\4=x[/tex]
So, NP[tex]=3x+4=3\times 4+4=12+4=16 cm[/tex]
