Question

A ramp represented by segment PQ in the figure below is used to load cargo on a truck. Maya wants to find the length of the ramp.



What is the length of the ramp used?

Answer 1

You have similar triangles there. How have you tried solving this?

Answer 2

i mean i dont know how

Answer 3

can you teach me?

Answer 4

OK, do you know the rule about similar triangles? Every heard about the ratio of the sides?

Answer 5

i know there is some rule but dont know it

Answer 6

OK. That is simple to show.

Answer 7

This is the rule about the ratio of the sides.

Answer 8

hmmm, i have to think about this

Answer 9

Now your triangles are drawn one atop the other, and they have a > drawn on the side that is not shared. That means it is parallel. That is why I say they are similar triangles.

Answer 10

okay so far so good

Answer 11

So, what would the ratio of the sides with the > mark be? It does not really matter which number you put on top.

Answer 12

they are parallel but without numbers idk the ratio of lengths

Answer 13

You can look at your original picture for the numbers.

Answer 14

ohhh 18/12 or 3/2

Answer 15

Yes. That is the ratio of the sides. Now, you have the unknown PQ and another side you can put into a related ratio. HOWEVER: Because you chose Larger\(\triangle\) over Smaller \(\triangle\) in the first ratio, you MUST use the same order in the second ratio.

Answer 16

so 3/2 times 16 gets me PS?

Answer 17

PQ*

Answer 18

Yes.

Answer 19

thank you!

Answer 20

And this is the one thing to be careful of:
These ratios would both get the right answer:
\[\frac{PR}{ST}=\frac{PQ}{SQ}\\
\frac{ST}{PR}=\frac{SQ}{PQ}\]
These would both get the WRONG answer:
\[\frac{PR}{ST}=\frac{SQ}{PQ}\\
\frac{ST}{PR}=\frac{PQ}{SQ}\]So as long as you are careful in setting up the ratios, these are not too hard.

Answer 21

awesome, thanks a lot!

Answer 22

Oh, and I got 24. Which I think you got too.

Answer 23

perfect