Question

Find x and the measures of the indicated parts.

A. X=3/2, AB =3

B. X=3/2, AB=6

C. X=14/3, AB=28/3

D. X=14/3, AB=28

Answer 1

A. X=3/2, AB =3

Explanation:

∆ADC ~ ∆AEB so we have AB/AC = AE/AD:

2x/(2x+4) = (14-8)/14

14(2x) = 6(2x+4) . . . . . . . cross multiply

28x = 12x +24 . . . . . . . . eliminate parentheses

16x = 24 . . . . . . . . . . . . . .subtract 12x

x = 24/16 = 3/2 . . . . . . . divide by the coefficient of x; reduce the fraction

Then the length of AB is ...

AB = 2x = 2(3/2) = 3

The solution is x = 3/2, AB = 3.