Question

What is the value of t? Points D and E are midpoints of the sides of triangle ABC. The perimeter of the triangle is 48 units. 0 2 MMIN O 3 B O 6 8 D 3t Α. 4t 7t + 6 C

Answer 1

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