Question

What is the length of AC?


3 ft

4 ft

9 ft

18 ft

Answer 1

18

Explanation:

Answer 2

Answer: The length of AC is 18 ft.

Explanation:

By the given diagram,

AM = MB and CN = NB

M and N are the mid points of the sides AB and CB respectively,

Thus, by the mid point theorem,

MN ║ AC,

By the alternative interior angle theorem,

∠BMN ≅ ∠BAC

∠BNM ≅ ∠BCA

Thus, by AA similarity postulate,

ΔBMN ≅ ΔBAC

By the property of similar triangles,

`(BM)/(BA)=(MN)/(AC)`

`(BM)/(BM+MA)=(MN)/(AC)`

`(4)/(4+4)=(9)/(AC)`

`(4)/(8)=(9)/(AC)`

`4AC=72\implies AC = 18\text{ ft}`

Thus, The length of AC is 18 ft.