Question

BE||CD. Find the value of x and AC.

Answer 1

x = 4.8

AC = 16.8

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.

`\frac{\text{AC}}{\text{AB}}=\frac{\text{AD}}{\text{AE}}`

`(x+12)/(12)=(10+4)/(10)`

`(x+12)/(12)=(14)/(10)`

10(x + 12) = 12 × 14

10x + 120 = 168

10x = 168 - 120

x = 4.8

AC = x + 4.8

= 12 + 4.8

= 16.8