what is the value of x

Question

what is the value of x

1. A.
2. 3
3. 
   
4. B.
5. 9
6. 
   
7. C.
8. 15
9. 
   
10. D.
11. 30

Answer 1

The two triangles are similar, so the ratios of their sides are equal:

(2x-10) / (x-3) = (2x-10 + 5) / (x-3 + 3)

(2x-10) / (x-3) = (2x-5) / x

Cross multiply and solve for x.

Answer 2

By triangle proportionality theorem:

(2x - 10) / 5 = (x - 3)/3

3(2x - 10) = 5x - 3)

6x - 30 = 5x - 15

x = 15 (C)

Answer 3

So Faiza A.,

Why wouldn't you ask, "How do I go about analysing this problem, so that I can solve it myself?"

If you had asked that, then I could point out to you that you have parallel segments at the bottom, which set up two similar triangles, and that you could easily do an identity for ratios of segments from the left to the right side, making them equal for two different positions of side segments: (labelling points A,B,C,D,E clockwise starting with the top vertex):

DE : BC :: AE : AB

Once you set that up as two fractions equal to each other, I think you would be able to take it from there. However, if you just insist on asking, "what is the value of x?" then I'm afraid you aren't ready to learn yet, and tutors would tend to NOT help you at all! Just sayin'.

-- Cheers, --Mr. d.