Hey there, 29levelupchaye2!
We know that a midsegment connects two midpoints of two of the sides of a triangle.
Example: Midpoint of side A connects midpoint of side B making midsegment DE
And that midsegment is parallel and half of the third side.
Example: Midsegment DE must be parallel to side C or third side of the triangle. Midsegment DE must be half of side C
So, in the problem it's given that the midsegment is
[tex]2x + 6[/tex]
And the side that is parallel to it is HI which is
[tex]5x + 9[/tex]
So,
[tex]5x + 9[/tex]
must be twice as
[tex]2x + 6[/tex]
since it's the midsegment.
[tex]5x + 9 = 2(2x + 6)[/tex]
I'm multiplying it by two since the midsegment is half of the side that is parallel.
Once distributed, you will get something like
[tex]5x + 9 = 4x + 12[/tex]
And now we solve for x
[tex]5x - 4x + 9 = 4x - 4x + 12[/tex]
[tex]x + 9 = 12[/tex]
[tex]x + 9 - 9 = 12 - 9[/tex]
[tex]x = 3[/tex]
So, the formula is
[tex]5x + 9 = 2(2x + 6)[/tex]
And distributed is
[tex]5x + 9 = 4x + 12[/tex]
And the solution is
[tex]x = 3[/tex]
Midsegment is 12 units
And the side is 24 units.
Thank you for using Brainly.
See you soon!
