Question

Please help I’m failing badly.

Answer 1

Check the picture below.

well, if we look at the picture above and the tickmarks, pretty much M and N are midpoints of their segment, that means that MN is the midsegment of the triangle whose base is JL. What the hell all that means? well, it means that MN is just half of JL.

`\stackrel{MN}{2x+5}=\cfrac{\stackrel{JL}{8x-18}}{2}\implies 4x+10=8x-18\implies 10=4x-18\implies 28=4x \\\\\\ \cfrac{28}{4}=x\implies 7=x\hspace{5em}\underset{MN}{\stackrel{2(7)+5}{\text{\LARGE 19}}}`

Answer 2

Answer: 19

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Step-by-step explanation:

The tickmarks tell us which segments are congruent (i.e. the same length).

We can see that:

JM = MK

because of the single tickmarks. Since these segments are the same length, we know that M is the midpoint of segment JK. The midpoint divides a segment into two equal pieces.

Similarly, N is the midpoint of segment LK.

Midpoints M and N join up to form midsegment MN.

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Rules:

1. The midsegment of a triangle is parallel to the side it doesn't go through.
2. The midsegment is half as long compared to the parallel side.

Rule 2 is what we'll focus on.

MN is half as long as the side JL.

This can be rephrased to: "JL is twice as long as MN".

So,

JL = 2*(MN)

8x-18 = 2*(2x+5)

8x-18 = 4x+10

8x-4x = 10+18

4x = 28

x = 28/4

x = 7

Then we can determine each segment length:

• MN = 2x+5 = 2*7+5 = 14+5 = 19 is the answer
• JL = 8x-18 = 8*7-18 = 56-18 = 38

Notice that JL = 38 is twice as long compared to MN = 19

Or you could say: JL/MN = 38/19 = 2, which helps verify the answer.