If rs is a midsegment of triangle hit and parallel to side hi, and rs is 2x + 6 and hi is 5x+9, write and solve an equation to find the lengths of the segments.

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

And the side that is parallel to it is HI which is

So,

must be twice as

since it's the midsegment.

I'm multiplying it by two since the midsegment is half of the side that is parallel.
Once distributed, you will get something like

And now we solve for x




So, the formula is

And distributed is

And the solution is

Midsegment is 12 units
And the side is 24 units.

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