Answer:
The length of segment DA is 15 units
Step-by-step explanation:
- The segment which joining a vertex of a triangle and the midpoint of the opposite side to this vertex is called a median
- The point of intersection of the median of a triangle divides each median into two parts the ratio between them is 1: 2 from the base, which means the length of the median is 3 times the part from the base
Let us use this rule to solve the question
In Δ AEC
∵ D is the midpoint of EC
∴ AD is a median
∵ B is the midpoint of AC
∴ EB is a median
∵ F is the midpoint of AE
∴ CF is a median
→ The three medians intersected at a point inside the triangle,
let us called it M
∵ AD ∩ EB ∩ CF at M
∴ M is the point of intersection of the medians of Δ AEC
→ By using the rule above
∴ AD = 3 MD
∵ MD = 5
∴ AD = 3(5)
∴ AD = 15 units
