Points D and E are midpoints of the sides of triangle ABC. The perimeter of the triangle is 48 units. What is the value of t?

A. 2

B. 3

C. 6

D. 8

9514 1404 393

  A.  2

Step-by-step explanation:

The perimeter is the sum of the side lengths:

  48 = (3t +3t) +(4t +4t) +(7t +6)

  42 = 21t . . . . . . . . . . . . . . . . . . . collect terms, subtract 6

  2 = t . . . . . . . . divide by 21

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for