Question

M75NL10What is the length of NP?OA. √76OB. √124OC. √174OD. 244P*not drawn to scale

Answer 1

Step 1:

Calculate MP

To calculate MP, we will use the formula below

`\begin{gathered} MP^2=ML^2+PL^2 \\ ML=7 \\ PL=10 \end{gathered}`

By substituting the values, we will have

`\begin{gathered} MP^(2)=ML^(2)+PL^(2) \\ MP^2=7^2+10^2 \\ MP^2=49+100 \\ MP^2=149 \\ MP=√(149) \end{gathered}`

Step 1:

Calculate PN

We will use the formula below

`\begin{gathered} PN^2=MN^2+PM^2 \\ MN=5,PM=√(149) \end{gathered}`

By substituting the values, we will have

`\begin{gathered} PN^(2)=MN^(2)+PM^(2) \\ PN^2=5^2+(√(149)^2) \\ PN^2=25+149 \\ PN^2=174 \\ PN=√(174) \end{gathered}`

Hence,

The final answer is

`\Rightarrow PN=√(174)`

OPTION C is the right answer