Question

What three lengths can NOT be the lengths of the sides of a triangle? a) 23 m, 17, m,14 m or b)11 m, 11 m, 12 m or c) 5 m, 7 m, 8 m or d) 21 m, 6 m, 10 m

Answer 1

Take each set of lengths and take two lengths at a time and add them together. If in one choice, any two lengths added together is not greater than the third length, that cannot be a triangle.

Answer 2

I did that I still can't find the answer

Answer 3

For example, here are two sets of lengths:
1) 13 cm, 12 cm, 18 cm
2) 5 in., 8 in., 15 in.

Let's work with set 1)
First, add each set of two lengths and compare to the third length.
a. 13 cm + 12 cm = 25 cm > 18 cm (ok)
b. 12 cm + 18 cm = 30 cm > 13 cm (ok)
c. 13 cm + 18 cm = 31 cm > 12 cm (ok)
Since each two lengths added together are greater than the third side, 13 cm, 12 cm, 18 cm can be a triangle.

Answer 4

they're all greater

Answer 5

No they are not.
Now let's do example 2).
a. 5 in. + 8 in. = 13 in. < 15 in. (not ok)
Just from that comparison, you can tell that set 2) will not make a triangle.

Answer 6

I see

Answer 7

You need to do one set at a time. Each set may need 3 additions and comparisons.

Answer 8

Here is your first choice:
a) 23 m, 17 m,14 m
What is 23 m + 17 m? Compare to 14 m
What is 17 m + 14 m? Compare to 23 m
What is 23 m + 14 m? Compare to 17 m

Answer 9

1. 40m 2. 31m 3. 37m

Answer 10

a) 23 m, 17 m,14 m
23m + 17 m = 40 m > 14 m (ok)
17 m + 14 m = 31 m > 23 m (ok)
23 m + 14 m = 37 m > 17 m (ok)
Choice a) makes a triangle. Now do the same to choices b), c), and d).

Answer 11

I'm so confused

Answer 12

You are correct. Now see that for each sum of two sides, I compared with the third side. Each sum was greater that the third side, so choice a) does make a triangle.

Answer 13

I don't know why you are confused.
You did the three sums correctly.

Answer 14

Now for each sum, compare it tot eh side you did not add.

Answer 15

Your three sums gave results:
1. 40 m
2. 31 m
3. 37 m
Right?

Answer 16

Yes

Answer 17

Now all you need to do is compare each sum to the side that was NOT added.
1. 40 m compared to 14 m
2. 31 m compared to 31 m
3. 37 m compared to 17 m
In each case, you see that the sum is greater than the third side right?

Answer 18

I do

Answer 19

yes all greater

Answer 20

Great. That means these three sides CAN make a triangle.
That means choice a) makes a triangle is not our answer.

Answer 21

Now we do the same for choice b)
We take each two sides at a time and add them. Then we compare the sum with the side we did not add.
I'll set it up for you.

Answer 22

so 22

Answer 23

11 plus 11

Answer 24

b)11 m, 11 m, 12 m
Let's drop the m (for meters) just to make it quicker to write).

Answer 25

Right. 11 + 11 compared to 12
11 + 11 = 22 > 12

Answer 26

So 22 is greater than 12

Answer 27

Since the sum is greater than the third side, it's good so far. We need to test the other possibilities.

Answer 28

Exactly.

Answer 29

so It's not going to be B correct?

Answer 30

Now we test 11 + 12 = ? and compare with 11

Answer 31

Correct. B is not it.
Now we move on to c).

Answer 32

c) 5 m, 7 m, 8 m
5 + 7 = ? compared to 8
7 + 8 = ? compared to 5
5 + 8 = ? compared to 7

Answer 33

Is each sum in b) greater than the third side?

Answer 34

1) 12 and 2) 15 and 3) 13

Answer 35

8 is the same

Answer 36

12 > 8
15 > 5
13 > 7
Each sum is greater than the third side.
Once again, c) works.

Answer 37

So now D

Answer 38

c) works meaning it makes a triangle, so it's not our answer.

Answer 39

I hate math because It takes forever to get done with just one problem

Answer 40

Now let's look at d)

Answer 41

21 m, 6m, 10m

Answer 42

d) 21 m, 6 m, 10 m

Answer 43

One way to shorten this type of problem is to look for a set of three sides in which one side is much larger than the other two.

Answer 44

21 is much larger then 6 and 10m

Answer 45

We just found it. Notice that 21 is much larger than 6 or 10.
Wow, you're ahead of me.

Answer 46

I think to much with math that's my problem

Answer 47

6 + 10 = 16, and 16 < 21
Set d) will not make a triangle, so we found our answer.

Answer 48

more then I have to

Answer 49

there we go!

Answer 50

thank you! you're patient, I'm terrible at math

Answer 51

We went through a long problem, but don't think it;'s a waste of time.
1) we did it together, and now you understand it.
2) after going through 3 choice that were not it, you got to practice that method a bit.
3) we figured out a quick way to do it: look for a set of sides that has one side much larger than the other two.

Answer 52

This is true, wow you're fantastic

Answer 53

You are very welcome, and thanks.
Keep practicing, studying & asking questions. That's how you learn.