Question

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

Explanation:

Step1: Identify the mid - segment theorem

In a triangle, if a line segment joins the mid - points of two sides of a triangle, then the line segment is parallel to the third side and half its length. 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

The length of the mid - segment $ML$ is related to the length of the side $VT$ by the formula $ML=\frac{1}{2}VT$. Given $ML = 12$. Let $VT$ be the side we want to find. Rearranging the formula for $VT$ gives $VT = 2\times ML$.

Step3: Calculate the length of $VT$

Substitute $ML = 12$ into the formula $VT=2\times ML$. So $VT = 2\times12=24$.

Answer:

B. 24