Question

c.) find length of || side of midseg.

Explanation:

Step1: Recall mid - segment theorem

The mid - segment of a triangle is parallel to the third side and its length is half of the length of the third side. Let the length of the mid - segment be $2x - 10$ and the length of the parallel side be $2x - 4$. According to the mid - segment theorem, $2(2x - 10)=2x - 4$.

Step2: Expand the left - hand side

$4x-20 = 2x - 4$.

Step3: Move the $x$ terms to one side

Subtract $2x$ from both sides: $4x-2x-20=2x - 2x-4$, which simplifies to $2x-20=-4$.

Step4: Solve for $x$

Add 20 to both sides: $2x-20 + 20=-4 + 20$, so $2x = 16$. Then divide both sides by 2: $x = 8$.

Step5: Find the length of the parallel side

Substitute $x = 8$ into the expression for the parallel side $2x - 4$. We get $2\times8-4=16 - 4=12$.

Answer:

12