When a line drawing from the mid-point of any triangle cuts the opposite side which is parallel to the third side, then the intersected point on the other side is always a mid point of that side. The required length of sides of the triangle [tex]\rm{HJ\;\&\;JE\;\rm{are} \;8\;and \;5 \;units[/tex] respectively.
Given:
In [tex]\Delta EFG[/tex], H is the midpoint of GE and J is the midpoint of FE.
From the figure, [tex]HJ\parallel GF[/tex] and H is the midpoint of GE and J is the midpoint of FE.
According to Mid-point theorem the line segment in a triangle joining the midpoint of two sides of the triangle is said to be parallel to its third side and is also half of the length of the third side.
[tex]GF=2HJ[/tex]
[tex]4x-4=2(x+3)\\4x-4=2x+6\\2x=6+4\\x=\frac{10}{2}\\x=5[/tex]
Now, the length of [tex]HJ=5+3=8\;\rm{unit}[/tex]
And, the length of [tex]JE=5-1=4\;\rm{unit}[/tex].
Therefore, the measure of lengths of [tex]HJ\;\&\;amp;\;JE\;\rm{are} \;8\;and \;5 \;units[/tex].
Learn more about the Mid-point theorem here:
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