SOLUTION: Points A, B, C, and D are collinear and positioned in that order. Find the length of CD, if CD = 3x+10, AB = 2x+15, AD = 7x+25 and BC = 24. Write your answer in small letter withou

Algebra ->  Length-and-distance -> SOLUTION: Points A, B, C, and D are collinear and positioned in that order. Find the length of CD, if CD = 3x+10, AB = 2x+15, AD = 7x+25 and BC = 24. Write your answer in small letter withou      Log On


   

Question 1190352: Points A, B, C, and D are collinear and positioned in that order. Find the length of CD, if CD = 3x+10, AB = 2x+15, AD = 7x+25 and BC = 24. Write your answer in small letter without space. For example x=10.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

given:
CD+=+3x%2B10
AB+=+2x%2B15
AD+=+7x%2B25+
BC+=+24

The segment addition theorem tells you that

+AB+%2BBC+%2BCD+=+AD.........substitute given values
2x%2B15%2B24%2B3x%2B10=7x%2B25........solve for x
5x%2B49=7x%2B25
49-25=7x-5x
24=2x
x=12

the length of CD is:
CD+=+3%2A12%2B10
CD+=+46