Solution:
Step 1:
Calculate MP
To calculate MP, we will use the formula below
[tex]\begin{gathered} MP^2=ML^2+PL^2 \\ ML=7 \\ PL=10 \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} MP^{2}=ML^{2}+PL^{2} \\ MP^2=7^2+10^2 \\ MP^2=49+100 \\ MP^2=149 \\ MP=\sqrt{149} \end{gathered}[/tex]
Step 1:
Calculate PN
We will use the formula below
[tex]\begin{gathered} PN^2=MN^2+PM^2 \\ MN=5,PM=\sqrt{149} \end{gathered}[/tex]
By substituting the values, we will have
[tex]\begin{gathered} PN^{2}=MN^{2}+PM^{2} \\ PN^2=5^2+(\sqrt{149)^2} \\ PN^2=25+149 \\ PN^2=174 \\ PN=\sqrt{174} \end{gathered}[/tex]
Hence,
The final answer is
[tex]\Rightarrow PN=\sqrt{174}[/tex]
OPTION C is the right answer
