Answer :
Perimeter = The sum of all sides of triangle
D & E are the mid points of AB & BC respectively
So, AD = BD
BE = EC
In the given triangle : AD = 3t, EC = 4t
AD = BD = 3t
BE = EC = 4t
and side AC = 7t + 6
So, the Perimeter of triangle ABC = AB + BC + CA
Perimeter of triangle ABC = AD + DB + BE + EC + CA
Substitute the value and simplify :
Perimeter of triangle ABC = AD + DB + BE + EC + CA
Perimeter of triangle ABC = 3t + 3t + 4t + 4t + 7t + 6
Perimeter of triangle ABC = 21t + 6
It is given that perimeter of triangle ABC is 48 units
So, 21t + 6 = 48
21t = 48 - 6
21t = 42
t = 42/21
t = 2
Answer : A) 2