Answer:
x = 5
AB = 14 units
Step-by-step explanation:
From the picture attached,
In the given triangles ΔAEB and ΔCDB,
AE║CD and ED is a transverse,
∠EAB ≅ ∠DCB [Alternate interior angles]
AE║CD and AC is a transverse,
∠AEB ≅ ∠CDB [Alternate interior angles]
ΔAEB ~ ΔCDB by AA property of the similarity of two triangles.
Therefore, corresponding sides of these triangles will be proportional.
[tex]\frac{\text{AE}}{\text{CD}}=\frac{\text{BE}}{\text{BD}}=\frac{\text{AB}}{\text{BC}}[/tex]
[tex]\frac{\text{BE}}{\text{BD}}=\frac{\text{AB}}{\text{BC}}[/tex]
⇒ [tex]\frac{7}{4}=\frac{2x+4}{x+3}[/tex]
⇒ 7x + 21 = 8x + 16
⇒ 8x - 7x = 21 - 16
⇒ x = 5
AB = (2x + 4)
= 10 + 4
= 14 units
