Question

How do I find nk how am I supposed to explain the lengths equal

Answer 1

The JK is perpendicular bisector of NL. So NJ = LJ.

Consider the triangle NJK and triangle LJK.

`NJ=LJ\text{ (JK is perpendicular bisector of NL)}`
`\angle NJK=\angle LJK\text{ (Each angle is 90 degree)}`
`JK=JK\text{ (Common side)}`

So triangle NJK is congruent to triangle LJK. So segment lengths that are equal,

`NK=LK`
`NJ=LJ`

2.

The equation for x,

`6x-5=4x+1`

Solve the equations for x.

`\begin{gathered} 6x-4x=1+5 \\ 2x=6 \\ x=3 \end{gathered}`

So the length of side NK is,

`\begin{gathered} NK=6\cdot3-5 \\ =18-5 \\ =13 \end{gathered}`

So the length of side NK is 13.