Question

Points D and E are midpoints of the sides of triangle ABC. The perimeter of the triangle is 48 units. Triangle A B C is shown. Point D is the midpoint of side A B and point E is the midpoint of side B C. The lengths of A D and D B are 3 t, the lengths of B E and E C are 4 t, and the length of A C is 7 t + 6. What is the value of t

Answer 1

9514 1404 393

Answer:

  t = 2 units

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  AD +DB +BE +EC +AC = 48 = 3t +3t +4t +4t +7t +6

  42 = 21t . . . . . . subtract 6 and simplify

  42/21 = t = 2 . . . . . . divide by the coefficient of t