Question

I'm terrible with ratios and similar triangles .-. please help.



The sides of a triangle are in the ratio of 1:2:2 and the perimeter of the triangle is 15 feet. The length of the shortest side is

Answer 1

A.2.5 feet

B.3 feet

C.5 feet

D.7.5 feet

An explanation would be nice as well

Answer 2

algebra?

Answer 3

No, Geometery.

Answer 4

but do you know algebra? :)

Answer 5

Yeah, I took that last year...I'm decent enough with it.

Answer 6

Okay, so we have the lengths of the triangle in a 1:2:2 proportion, any idea what that means? :)

Answer 7

Is it bad I don't?

Answer 8

Nope. We all didn't know what that meant some time ago. But after I'm done with you, you'll know what it means (I hope ^.^)

Answer 9

And it helps a lot that you know algebra.

Ready to get started?

Answer 10

As ready as I can be

Answer 11

Good.
The sides of the triangle are in a proportion of 1:2:2
This doesn't tell us the lengths of the sides, so, it tells us only this...
The side corresponding to the "1" is the SHORTEST side, and the two sides that correspond the two "2"s are the 'longer' sides.

getting it?

Answer 12

So far yes.

Answer 13

What the 1:2:2 tells us is that the longer sides are TWICE as long as the shortest side.

If that wasn't clear, I'll give you another case: If the proportion was 1:2:3 instead, this indicates that you have a shortest side, "1", a side TWICE as long as the shortest side, "2", and a side THREE TIMES as long as the shortest side, "3"

still getting it?

Answer 14

Yeah so if we had lengths it would be something like: 3, 6, and 6 again?

Answer 15

Seems like you already have your answer :D

Answer 16

Though, if you like, I could demonstrate how to formally arrive at that answer ^.^

Answer 17

Okay now I'm confused /_\

Answer 18

Scratch what I said, I'll go through the details.

But you understood my point about proportions right, and how the two longer sides are twice as long as the shortest side because of 1:2:2?
^.^

Answer 19

Yeah, wish my teacher had said that.

Answer 20

Okay.
Again, we don't know (yet) the length of the shortest side, so for now, we'll call it x, okay? ^.^

Answer 21

Yeah, it's a variable.

Answer 22

Right. If the shortest side is x, what about the other two sides?

Answer 23

Y and Z?

Answer 24

no... we know for a fact that those two sides are TWICE as long as the shortest side x.

So, the other two sides should be 2x, each.

agreed?

Answer 25

Oh, Yeah. I thought you meant name them. >_<

Answer 26

We're almost done.
The sides of the triangle are x, 2x, and 2x.

AND they add up to 15.

So we have
x + 2x + 2x = 15

Get your algebra up, solve for x.

Answer 27

Oh, equations are easy. So, X=3?

Answer 28

Yes.
And you remember, we defined x to be the length of the shorter side, earlier.

So that's your answer, finally :)

Answer 29

Thank you!

Answer 30

So... you have an idea what 1:2:2 mean now, right?
I didn't fail you right?
^.^

Answer 31

Yeah, If the ratio was 1:7:9 it would be 7 times as long as 1, and 9 would be 9?

Answer 32

That is correct :)

There ARE extremely minor issues with ratios that don't have a 1 in them... all in good time, I suppose :D

Answer 33

Thanks, you may have just taught better than my last two math teachers. .-.

Answer 34

students (kids) are more understanding, in general XD
how old are you anyway? :)

Answer 35

15, going to be a junior.

Answer 36

My teacher Sophomore year (last year) was the head football coach and spent most class time dealing with that, it was kinda annoying actually.

Answer 37

And Freshman year the state I'm in decided to try this new math class, unfortunately I was a guinea pig. Barely passed with a 73.

Answer 38

football coach for a maths teacher? interesting situation :)

Answer 39

Yeah...Most the people in our class failed...

Answer 40

Not the class I mean, but our state EOCT.

Answer 41

that's a shame. my experience shows students are more responsive to fellow students (hence this site lol)

I didn't expect you to be so advanced though... I guess when you advance so far, you forget the easier stuff ^.^

Answer 42

Yeah, we reviewed some pretty simple stuff last year I knew I excelled in before, but I forgot most of it between the classes.

Answer 43

but this partitive proportion is fifth grade stuff, isn't it? :D
(ignoring for the moment that this involves geometry somewhat, probably~ you didn't actually disclose the context of this problem haha )

Answer 44

Yeah, after you explained it I was like >_< wow how did I not get that.

Answer 45

But because I failed the EOCT I have to retake it, but they won't let me unless I re-do the whole class.

Answer 46

i would try an help but my math teacher sucks now im here'

Answer 47

Me and him had the same teacher >.<

Answer 48

true he was all like the answer is below

Answer 49

he was dumb

Answer 50

well, I'm here if you need me, but don't expect too hardcore stuff, I'm one year below you lol :D

Answer 51

Skrilluh is typing..

Answer 52

Woah What!? a Sophomore? .-. :-: now I really feel bad.

Answer 53

hes done

Answer 54

Don't... we all have our downtimes

Answer 55

:D

Answer 56

Lol X3