Answer:
With the assumption that the line FD passes through the point B, we have;
y = 7
x = 6
Explanation:
The given parameters are;
Line FD bisects segment AC
Therefore, segment AE = segment EC By definition of line AC which is bisected by the line FD
Segment ED ≅ Segment ED by reflexive property
∠CED = ∠AED = 90° (Angles formed by a perpendicular bisector (FD) to a line (AC))
Therefore;
ΔCDE ≅ ΔADE by Side-Angle-Side (SAS) rule of congruency
From which we have;
Segment CD ≅ Segment AD Congruent Parts of Congruent Triangles are Congruent (CPCTC)
Segment CD = Segment AD Definition of congruency
∴ 12·y - 8 = 8·y + 20 by substitution property
12·y - 8·y = 20 + 8
4·y = 28
y = 28/4 = 7
y = 7
From segment AE = segment EC, we have;
2·x + 4·y = 2·x + 4·y by substitution property
2·x + 4×7 = 2·x + 4×7 by substitution property
Segment AE = 2·x + 28 = Segment EC
Segment AC = Segment AE + Segment EC by definition of segment (AC) bisected by a line (FD)
∴ Segment AC = 2·x + 28 + 2·x + 28 = 4·x + 56 by substitution property
Segment CD = 8·y + 20 = 8 × 7 + 20 = 56 + 20 = 76
Segment CD = 76
The sides of the ΔABC are;
Segment BC = 6·x + 18
Segment BA = 8·x + 6
Segment AC = 4·x + 56
With the assumption that the Line FD passes through the point B, we have;
Segment BC = Segment AB by congruent triangles ΔABE ≅CBE based on Side-Angle-Side (SAS) rule of congruency
Therefore;
6·x + 18 = 8·x + 6
18 - 6= 8·x - 6·x = 2·x
2·x = 18 - 6 = 12
x = 12/2 = 6
x = 6