A line parallel to a triangle's side splits AB into lengths of x − 6 and x + 1. The other side, AC, is split into lengths of x a

Question

2 years ago

9

A line parallel to a triangle's side splits AB into lengths of x − 6 and x + 1. The other side, AC, is split into lengths of x a

nd x + 21. What is the length of AC?
A)27
B)33
C)39
D)45
Please explain how you solved. Do not comment unless you are sure you know the answer. I will give you brainliest for right answer.

Mathematics

2 answers:

MrRa [10] · Answer 1 · 2022-07-24T01:49:57+03:00

MrRa [10]2 years ago

6 0

Answer:

AC=39

Step-by-step explanation:

Aleks [24] · Answer 2 · 2022-07-23T23:27:31+03:00

AC = 39

Side Am/mB (x + 1)/(2x - 5)
Side Am/mC (x + 21)/(2x + 21)
m is the point where the parallel line is.
AB = AC
(x+1)/(2x -5) =(x +21)/(2x+21)
Cross multiply.
(x+1)(2x+21)=(2x-5)(x+21)
2x^2+23x+21=2x^2+37x-105
Subtract 2x^2 from both sides.
23x+21=37x-105
Subtract 23x from both sides.
21= 14x -105
Add 105 to both sides
126 = 14x
Divide both sides by 14
x = 9
Plug 9 back in for x in
2x + 21
2(9) + 21 = 39