Question

Find the value of LK

Answer 1

`\sf \: LK = 7 \: units`

Explanation:

It's clear that,

`\sf \: NM + ML + LK = NK`

Given that,

NM ---> x - 6

ML ---> 9

LK ---> 2x - 19

NK ---> 23

First, let us find the value of x using these values.

`\sf \: NM + ML + LK = NK \\ \sf x - 6 + 9 + 2x - 19 = 23 \\ \sf \: combine \: like \: terms. \\ \sf \: 3x - 16 = 23 \\ \sf3x = 23 + 16 \\ \sf3x = 39 \\ \sf \: divide \: both \: sides \: by \: 3. \\ \sf \: x = 13`

And now we have to find out the length of LK.

As we mentioned before,

LK = 2x - 19

So, to find the length of LK, we have to replace x with 13 and solve the equation.

Let us solve now.

`\sf \: LK = 2x - 19 \\ \sf \: LK = 2 * 13 - 19 \\ \sf \: LK = 26- 19 \\ \sf \: LK = 7 \: units`

Answer 2

LK = 7

Explanation:

We are using segment addition

NM + ML + LK = NK

x-6 + 9 + 2x-19 = 23

Combine like terms

x+2x -6+9-19 = 23

3x -16 = 23

Add 16 to each side

3x-16+16 = 23+16

3x = 39

Divide each side by 3

3x/3 = 39/3

x = 13

We want to find the value of LK

LK = 2x-19

=2(13) -19

= 26 -19

= 7