Point B is on line segment \overline{AC} AC . Given AB=2x+10,AB=2x+10, BC=x,BC=x, and AC=5x,AC=5x, determine the numerical length of \overline{AC}. AC .

Answer 1

Point B is on line segment \ overline AC . Given AB=2x+10, BC=x, and AC=5x, determine the numerical length of \ overline AC= ??

Detailed Solution:

AB = 2x + 10 BC = x AC = 5x

A======================================================B==============C

AC = AB + BC

(5x) = (2x + 10) + (x)

5x = 3x + 10

5x – 3x = 10

2x = 10

x = 5

Therefore:

AB = 2x + 10 ==> AB = 2(5) + 10 ==> AB = 10 + 10 ==> AB = 20

BC = x ==> BC = (5) ==> BC = 5

AC = 5x ==> AC = 5(5) ==> AC = 25

Check: AC = AB + BC ==> 25 = 20 + 5 ==> 25 = 25