Question

AC=4, AE=7, AD=10, what is the length of AB?

A: 1 3/7
B: 2 1/2
C: 5 5/7
D: 17 1/2

Answer 1

C.
`AB = 5(5)/(7)`

Explanation:

When two polygons are considered similar, the ratio of their corresponding sides would also be equal.

Since ∆ABC and ∆ADE are similar,
`(AE)/(AC) = (AD)/(AB)`

`(7)/(4) = (10)/(AB)`

Cross multiply

`7*AB = 10*4`

`7*AB = 40`

Divide both sides by 7 to find AB

`(7*AB)/(7) = (40)/(7)`

`AB = (40)/(7)`

`AB = 5(5)/(7)`