Answer:
AB = 14 units
Step-by-step explanation:
Given:
A triangle GHJ with the following aspects:
A, B, C are midpoints of sides GH, HJ and GJ respectively.
AB = [tex]3x+8[/tex]
GJ = [tex]2x+24[/tex]
Midsegment Theorem:
The line segment joining the midpoints of any two sides of a triangle is parallel to the third side and the length of the midsegment is one-half of the length of the third side.
Therefore, AB is the midsegment of sides GH and HJ and thus, is parallel to GJ and equal to one-half the length of GJ.
[tex]\therefore AB=\frac{1}{2}\times\ GJ[/tex]
Now, plug in the values of AB and Gj and solve for 'x'.
This gives,
[tex]3x+8=\frac{1}{2}(2x+24)\\\\3x+8=x+12\\\\3x-x=12-8\\\\2x=4\\\\x=\frac{4}{2}=2[/tex]
Now, the length of AB is given by plugging in 2 for 'x'.
[tex]AB=3\times2+8=6+8=14[/tex]
Therefore, the length of midsegment AB is 14 units.
