find tv.\n a. 6\n b. 24\n c. 12\n d. 48

Explanation:

Step1: Identify mid - segment theorem

In a triangle, if a line segment joins the mid - points of two sides of a triangle, it is parallel to the third side and its length is half of the length of the third side. Here, $ML$ is a mid - segment of $\triangle UVT$ since $M$ is the mid - point of $UV$ and $L$ is the mid - point of $UT$.

Step2: Apply the mid - segment formula

Let $ML$ be the mid - segment and $TV$ be the third side. The formula is $ML=\frac{1}{2}TV$. Given $ML = 12$. We can solve for $TV$ by multiplying both sides of the equation by 2. So, $TV = 2\times ML$.

Step3: Calculate the value of $TV$

Substitute $ML = 12$ into the equation $TV=2\times ML$. Then $TV = 2\times12=24$.

Answer:

B. 24