Answer:
x = 4.8
AC = 16.8
Step-by-step explanation:
From the picture attached,
In ΔABE and ΔACD
BE║CD, and the AC and AD are the transversal lines.
∠ABE ≅ ∠ACD [Corresponding angles]
∠AEB ≅ ∠ADC [Corresponding angles]
ΔABE ~ ΔACD [By AA property of similarity of two triangles]
And by the property of similar triangles, corresponding sides of the similar triangles are always proportional.
[tex]\frac{\text{AC}}{\text{AB}}=\frac{\text{AD}}{\text{AE}}[/tex]
[tex]\frac{x+12}{12}=\frac{10+4}{10}[/tex]
[tex]\frac{x+12}{12}=\frac{14}{10}[/tex]
10(x + 12) = 12 × 14
10x + 120 = 168
10x = 168 - 120
x = 4.8
AC = x + 4.8
= 12 + 4.8
= 16.8
