## jaylelile one year ago AB:BC is 3:4. Solve for x. A.11 B.14 C.120 D.140

1. jaylelile

2. jaylelile

3. mathstudent55

You are given this, right? $$\dfrac{AB}{BC} = \dfrac{3}{4}$$

4. jaylelile

right..

5. mathstudent55

Now replace AB and BC with the lengths given in the figure. What do you get?

6. jaylelile

|dw:1433800191984:dw|

7. mathstudent55

$$\dfrac{90}{10x-20} = \dfrac{3}{4}$$ Ok?

8. jaylelile

oh okay

9. mathstudent55

-20 is not the length of BC. The entire expression 10x - 20 is. See my equation above?

10. mathstudent55

Now we solve that equation.

11. mathstudent55

When you have a fraction equal to a fraction, you can cross multiply.

12. mathstudent55

|dw:1433800210299:dw|

13. jaylelile

so x=14?????

14. mathstudent55

|dw:1433800248981:dw|

15. jaylelile

x=14 right?

16. jaylelile

I just have a hard time making the equations.

17. jaylelile

Can you help me with a few more questions?

18. mathstudent55

Now we cross multiply in our problem. $$3(10x - 20) = 4(90)$$ $$30x - 60 = 360$$ $$30x = 420$$ $$x = 14$$ You are correct.

19. jaylelile

yay! Thank you so much! Can you help me with a few more? I get confused when it comes to setting up the equations.

20. mathstudent55

Let's see if our answer makes sense. Sides AB and BC are in a 3:4 ratio. Side AB measures 90. Side BC measures 10(x) - 20. We know x = 14, so side BC measure 10(14) - 20 = 140 - 20 = 120. Side BC measures 120. Since AB:BC = 3:4, then 90:120 also has to be a 3:4 ratio. $$\dfrac{90}{120} = \dfrac{30 \times 3}{30 \times 4} = \dfrac{3}{4]$$ We are correct. x = 14 makes sense.

21. jaylelile

Find the value of x. A. 7 B. 9 C. 11 D. 12

22. mathstudent55

Do you know the triangle angle bisector theorem?

23. mathstudent55

The angle bisector of an angle of a triangle divides the opposite side in two segments whose lengths are proportional to the lengths of the other sides of the triangle, each segment to its adjacent side.

24. jaylelile

I just don't know how to write an equation to solve.

25. mathstudent55

That is a very cumbersome way to express this: |dw:1433800821218:dw|

26. mathstudent55

Compare the above figure to your problem.

27. mathstudent55

|dw:1433801007502:dw|

28. mathstudent55

Here is the fugure from your problem with the letter "y" added.

29. mathstudent55

The angle at the right was bisected. That means look at the segments on the opposite side. The segments are x and y. Ok?

30. jaylelile

I'm not really following....

31. jaylelile

wait! So it would be 9??? I think I'm understanding.

32. mathstudent55

According tot he theorem, the segments are proportional to the adjacent sides, so you can write this: $$\dfrac{36}{x} = \dfrac{28}{y}$$

33. jaylelile

so it isn't 9?

34. mathstudent55

Now we need to express y in terms of x. Notice the left side is 16. One segment in it is x, so the other segment is 16 - x. That is the segment I called y. $$\dfrac{36}{x} = \dfrac{28}{16 - x}$$ Now you cross multiply and solve for x.

35. mathstudent55

28x = 36(16 - x) 28x = 576 - 36x 64x = 576 x = 9

36. mathstudent55

You are correct.

37. jaylelile

YAY!!! Thanks! can you help me with one more?

38. jaylelile

last one: Find the value of each variable. A. a = 15, b = 5, c = 8, d = 4 B. a = 15, b = 4, c = 8, d = 5 C. a = 14.5, b = 5, c = 6, d = 4 D. a = 14.5, b = 4, c = 6, d = 5

39. mathstudent55

Ok, here there is another thing at work. If you have two lines that are cut by parallel lines, the segments are of proportional lengths. That means $$\dfrac{d}{5} = \dfrac{12}{15} = \dfrac{c}{10}$$

40. mathstudent55

Use the left two fractions as a proportion and solve for d. Then use the right two fractions as a proportion and solve for c

41. mathstudent55

Do you understand what to do?

42. jaylelile

yes! Thank you very much for all your help!

43. mathstudent55

You're welcome.