in a diagram of a scalene triangle ABC, line DE is the midpoint of line AB and line AC and DE=7 find the length of line BC

To find the length of line BC in a diagram of a scalene triangle ABC, where line DE is the midpoint of line AB and line AC, and DE = 7, we can use the concept of similar triangles.

1. First, let's label the diagram. Triangle ABC has vertices A, B, and C. Line DE is the midpoint of line AB, so points D and E divide AB into two equal segments.

2. Since DE is the midpoint, we know that AD = DB. Let's label AD and DB as x each.
Therefore, AB = AD + DB = x + x = 2x.

3. Now, let's look at triangle ABC. By the Midpoint Theorem, line DE is parallel to line AC, and it divides line AB into two equal segments. This creates two similar triangles: triangle ADE and triangle ABC.

4. Since triangles ADE and ABC are similar, their sides are proportional. We can set up a proportion using the corresponding sides:
(DE/AD) = (BC/AB)

Plugging in the given values, we have:
7/x = BC/2x

5. To solve for BC, we can cross-multiply and solve the resulting equation:
7 * 2x = x * BC
14x = x * BC

6. Cancel out the common factor of x:
14 = BC

Therefore, the length of line BC is 14 units.