Final answer:
C. t=4 Expressing these lengths as 't,' the equation 2*(t + t + t) = 48 represents the perimeter. Solving for 't' yields t = 4, indicating that the value of /t is 4, as the equal segments formed by the midpoints have a length of 4 units each."
Explanation:
Given that points D and E are midpoints of the sides of triangle ABC, and the perimeter of the triangle is 48 units, the value of /t can be calculated using the concept that the midpoints of a triangle divide its sides into segments of equal length. As D and E are midpoints, they divide each side of the triangle into segments of equal length.
This means that the segments AD, BD, BE, and CE are all of equal length. Hence, the perimeter of the triangle can be expressed as 2 times the sum of AD, BD, and BE. If we denote the length of each of these segments as 't,' then the perimeter can be written as 2*(t + t + t) = 48. Solving this equation gives t = 4. Therefore, the value of /t is 4.
Triangles with midpoints on their sides create segments of equal length, forming smaller triangles within the original triangle. These smaller triangles have sides that are half the length of the original triangle's sides. Consequently, the perimeter of the original triangle, ABC, equals twice the sum of the lengths of segments AD, BD, and BE, as these segments collectively cover the entire perimeter.
Expressing these lengths as 't,' the equation 2*(t + t + t) = 48 represents the perimeter. Solving for 't' yields t = 4, indicating that the value of /t is 4, as the equal segments formed by the midpoints have a length of 4 units each."