1. In triangle ABC, D is the midpoint of BC. If Ac = 3x-15 and DE =6, what is the value of x?
A. 6
B. 7
C. 9
D. 12

Option C. 9

Step-by-step explanation:

The question is as following:

In triangle ABC, D is the midpoint of line AB and E is the midpoint of line BC. If AC= 3x-15 and DE= 6, what is the value of x?

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See the attached figure which represents the problem.

As shown:

D is the midpoint of line AB ⇒ AD = DB

E is the midpoint of line BC  ⇒ BE = EC

Apply The Mid-segment theorem which states that the mid-segment connecting the midpoints of two sides of a triangle is parallel to the third side of the triangle, and the length of this mid-segment is half the length of the third side.

So, DE = 0.5 AC

Given: Ac = 3x-15 and DE =6

∴ 6 = 0.5 (3x - 15)

solve for x

Multiply both sides by 2

12 = 3x - 15

3x = 12 + 15 = 27

x = 27/3 = 9

So, the value of x is 9

The answer is option C. 9