Final answer:
To find the length of AB with T as the midpoint, we add the lengths of AT and TB. Since T is the midpoint, AT and TB are equal, thus AB is twice the length of AT or TB resulting in AB being 728x+.
Step-by-step explanation:
To find the length of the segment AB given that T is the midpoint, we simply add the lengths of AT and TB, since the midpoint divides the segment into two equal parts. As given, AT = 364x+ and TB = 192x+. Because T is the midpoint, we know that AT = TB, so we set them equal to each other:
364x+ = 192x+.
By simplifying this equation, we can solve for x, but since both expressions are already equal due to the midpoint property, we find that AB = AT + TB = 2(AT) or 2(TB).
In this case, it would be:
AB = 2(364x+) = 728x+