Question

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.

Answer 1

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
$2x + 6$
And the side that is parallel to it is HI which is
$5x + 9$
So,
$5x + 9$
must be twice as
$2x + 6$
since it's the midsegment.
$5x + 9 = 2(2x + 6)$
I'm multiplying it by two since the midsegment is half of the side that is parallel.
Once distributed, you will get something like
$5x + 9 = 4x + 12$
And now we solve for x
$5x - 4x + 9 = 4x - 4x + 12$
$x + 9 = 12$
$x + 9 - 9 = 12 - 9$
$x = 3$
So, the formula is
$5x + 9 = 2(2x + 6)$
And distributed is
$5x + 9 = 4x + 12$
And the solution is
$x = 3$
Midsegment is 12 units
And the side is 24 units.

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