Question

XYZ is a triangle with side lengths in the ratio 2 : 3 : 4. The perimeter of XYZ is 27 yards. Find the length of the shortest side.

Answer 1

I Really Need help!! <3

Answer 2

Ok, let me see if I can explain this the right way. We have the perimeter of the triangle which is equal to all the sides added together, right? So we add side a, side b, side c = 27. But it would help if we could use one variable for all the sides so we could solve for the variable and find all the lengths, right? Well, good news...you can do that. I'll show you how.

Answer 3

We will call the short side with the ratio of 2 "x". The longest side, the one with the 4 ratio, is twice as long as the shortest side, so we will call that "2x". The 3 ratio side is 1.5 times the shortest side so we will call that 1.5x. Now we will add them all together and set it to equal 27. All the same variable now.

Answer 4

x + 1.5x + 2x = 27. When we solve this for x we will find the length of the shortest side.

Answer 5

4.5x = 27
x=6

Answer 6

So the shortest side is 6 units long. The inbetween one is 1.5 times that, so 6(1.5) = 9, and the longest side is twice the length of the shortest side, so the longest side measures 12. Let's add this up to see if it works...6+9+12=27. It worked! Yay!

Answer 7

Yes, I can help you.

Answer 8

ABCD is a rectangle with side lengths as shown in the figure. Write the ratio of the side lengths in the form AB : BC : CD : DA.

Answer 9

I'm assuming you are posting a picture or something, right?

Answer 10

it looks like that

Answer 11

Well the side that measures 5 is 1 2/3 times larger than the smaller side. So the ratios are \[\frac{ 5 }{ 3 }:1:\frac{ 5 }{ 3 }:1\]

Answer 12

You make the smaller side into a 1, then the bigger side is how many times bigger than the smaller. That is how you make a proportion or a ratio.

Answer 13

Notice that if you multiply the 5/3 and the 1 by 3 you get back your 5 and your 3 in the original rectangle.

Answer 14

the answer options are:
1. 5:3 5:3
2. 5:5 3:3
3. 3:5 3:5
4. 3:3 5:5

Answer 15

Oh, ok, then, they did it the totally easy and cheesy way and it is 1. That is your answer. I based it on the shortest side being "1". But they didn't. They literally took the side measurements and made them into ratios. Your answer is #1.

Answer 16

Ok! perfect! :) I do have a couple more questions I dont really get, if you dont mind :)

Answer 17

Ok, shoot...

Answer 18

Baking a cake here with my daughter as I do this...so bear with me! ; )

Answer 19

x+3/4= 9/x+3

Answer 20

Solving for x, right?

Answer 21

Oh ok, no worries! :) and it says solve the proportion

Answer 22

Is it this:\[\frac{ x+3 }{ 4 }=\frac{ 9 }{ x+3 }\]

Answer 23

the options are
1. 18 or -8
2. 9 or -9
3. 3 or -3
4. 3 or -9

Answer 24

So by the looks of your answer options, I'm thinking what I typed was correct. Yes?

Answer 25

Yes it looks just like how you wrote it

Answer 26

Ok, then you will cross multiply. Just a quick hint: when you have a fraction that is equal to another fraction, you will ALWAYS cross multiply through the equals sign, ok?

Answer 27

Ok, that makes sense