*Triangle Midsegmet Theorem, I have a problem please help?

Question

In ΔGHL, K is the midpoint of segment LG, and J is the midpoint of segment LH. Find KJ.

KJ= 2x + 2

*This is the triangles corresponing base*
GH= 5x - 3

According to the Triangle Midsegment Theorem for any triangle -

The length of the midsegment is equal to one-half the length of its corresponding base.

But this problem is confusing, can someone please help me and answer this problem step by step and explain please.

You will be very helpful


Thanks

Answer 1

KJ is the midsegment of the triangle. Since the midsegment is 1/2 the corresponding base, that means we can take 2(KJ)=GH
Fill in values
2(2x + 2) = 5x - 3
4x + 4 = 5x - 3 Distribute
4 = x - 3 Subtract 4x from both sides
7 = x Add 3 to both sides

Now substitute back in to find KJ: 2(7) + 2 = 16

Answer 2

So KJ is the midsegment and GH is the corresponding base
so according to the theorem KJ=1/2GH
we know KJ=2x+2 and GH= 5x-3 so:
2x+2 = 1/2(5x-3)
4x+4=5x-3
x=7
so the length of the triangles midsegment is KJ=2*(7)+2 = 16
and the base GH=5*(7)-3=32

Answer 3

KJ = .5GH
2x+2 = .5(5x-3)
2x+2 = 2.5x -1.5
-.5x = -3.5
x = 7
KJ = 2(7)+2 = 16