Answer:
The length of Midsegment = 9
Step-by-step explanation:
the midsegment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this midsegment is half the length of the third side.
According to the Midsegment Theorem:
- The midsegment connects the midpoints of two sides of a triangle is parallel to the third side of the triangle.
- The length of this midsegment is half the length of the third side.
Thus,
The midsegment (x+4) is half the length of the third side (4x-2). so
[tex]\left(x+4\right)\:=\:\frac{1}{2}\:\left(4x\:-\:2\right)[/tex]
[tex]x+4=2x-1[/tex]
Subtract 4 from both sides
[tex]x+4-4=2x-1-4[/tex]
[tex]x=2x-5[/tex]
Subtract 2x from both sides
[tex]x-2x=2x-5-2x[/tex]
Simplify
[tex]-x=-5[/tex]
divide both sides by -1
[tex]\frac{-x}{-1}=\frac{-5}{-1}[/tex]
Simplify
[tex]x=5[/tex]
As
The length of Midsegment = x+4
= (5) + 4 ∵ x = 5
= 9
Therefore, the length of Midsegment = 9
