Calculate unknown length from known ratio

[AlaskaR]

AB is seperated by C by 5:7, and AB is seperated by D by 5:11. The length of CD is 5cm. What is the length of AB?

 

[Harry_the_cat]

Have you drawn a diagram.

 

[AlaskaR]

Have you drawn a diagram.

Yes but I am unsure if it is right. It would be better if someone thought of a diagram anew , but if you really want to know

 

[HallsofIvy]

To start with, take the length of AB to be "1". Then AC is 5/(5+7)= 5/12 and AD is 5/(5+ 11)= 5/16. In these coordinates, CD is 5/12- 5/16= 20/48- 15/48= 5/48.

The actual length of CD is 5 cm which is 5/48 times 48 cm. The actual length of AB is 1 times 48 or 48 cm.

 

[AlaskaR]

To start with, take the length of AB to be "1". Then AC is 5/(5+7)= 5/12 and AD is 5/(5+ 11)= 5/16. In these coordinates, CD is 5/12- 5/16= 20/48- 15/48= 5/48.

The actual length of CD is 5 cm which is 5/48 times 48 cm. The actual length of AB is 1 times 48 or 48 cm.

Thank you very much!