Question

Please solve quick ​

Answer 1

x = 5

AB = 14 units

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.

`\frac{\text{AE}}{\text{CD}}=\frac{\text{BE}}{\text{BD}}=\frac{\text{AB}}{\text{BC}}`

`\frac{\text{BE}}{\text{BD}}=\frac{\text{AB}}{\text{BC}}`

⇒
`(7)/(4)=(2x+4)/(x+3)`

⇒ 7x + 21 = 8x + 16

⇒ 8x - 7x = 21 - 16

⇒ x = 5

AB = (2x + 4)

= 10 + 4

= 14 units