Question

Can someone please help me how to do this and confuse and I don't get it

Answer 1

Based on the information given in the exercise, the segment JK, the segment KL and the segment LM are congruent, which means that they have equal length:

`JK\cong KL\cong LM`

You can identify that:

`\begin{gathered} JK=5x-28 \\ LM=2x+14 \end{gathered}`

Knowing that, you can set up the following equation:

`5x-28=2x+14`

Now you must solve for "x":

`\begin{gathered} 5x-28=2x+14 \\ 5x-2x=14+28 \\ 3x=42 \\ x=14 \end{gathered}`

You can substitute the value of "x" into the expression that represents the length of the segment JK or you can also substitute it into the expression that represents the length of the segment LM. You get:

`\begin{gathered} LM=2(14)+14 \\ LM=28+14 \\ LM=42 \end{gathered}`

Since:

`JK\cong KL\cong LM`

You can determine that:

`KL=42`

The answer is: Option A.