Question

I have always had trouble with these kinds of problems. How would you find x?

Answer 1

Would X just be 12?

Answer 2

What do the number represent, lengths or angles? Is X an angle or length? Are the horizontal lines parallel to each other?

Answer 3

Well they have the || marking on the diagram. But it is not stated in the problem. X is the line length.

Answer 4

I was thinknig since they are || then they would be the same but I am not sure because 24 does not equal 36 so 12 might not equal x the options are A.8 B.12 C.6 and D.2

Answer 5

If all horizontal lines are parallel, then 12 and 36 should be to each other as x and 24 are (i.e. x/24 = 12/36) since the lines are congruent to each other

Answer 6

So how would I set up the proportion?
24 36
___=___
x 12
?

Answer 7

Actually, the lines are similar, since x and 12 are related by a scaling factor (24/36), congruence is if both sides were the same length

Answer 8

cross multiply to get
288=36x
then get 8?

Answer 9

yes, that's how you would set it up, but key point is that one side's ratio is related to the other because they are similar

Answer 10

That's what I got, too. 8

Answer 11

Awesome, thanks so much for the help :)

Answer 12

np good luck

Answer 13

I just checked using a graphical geometry tool and our approach works for other lengths. The answer 8 is correct.

Answer 14

fantastic

Answer 15

One more thing. I just found justification for using this technique. I'll draw the picture and tell me if you can find how we can use similarity of triangles. I went through a whole process of laws of sines and in the end saw the similarity of triangles, which is a much simpler approach. Let me draw it. I'll check in later to see if you see the justification process.