Question

Really need help with inequalities in one triangle. WILL GIVE MEDAL


Here is the activity:

Answer 1

. Choose two straws and measure the length of each straw. Be sure to include units.
Each straw represents the side of a triangle.
2. Put the pipe cleaner halfway into the end of one straw. Then, put the other straw on
the other half of the pipe cleaner so that the straws are just touching. Bend the pipe
cleaner to make an angle.
3. Open and close the angle along the ruler to determine two possible lengths for a third
straw that could be the third side of a triangle.
4. Open and close the angle along the ruler to determine two lengths for a third straw that
would not work for the third side of a triangle.
5. Let the length of the third side of the triangle be x. Write an inequality to show the
longest and shortest possible lengths for the third side.

Answer 2

need to find 4 different straw lengths
4 possible lengths for a third side
4 impossible lengths for a third side
and 2 inequalities

Answer 3

The idea is that if you are making a triangle, you have three pieces. If you add the two smaller sides and they are less than (shorter than) the longer side. You can't make a triangle. It's called the triangle inequality.
Do it on paper for a minute. Make a base that is wide. Then make a little short side coming up from the left. And a little short side coming up from the right. They would never meet, even if you tried to aim them at each other.

Answer 4

So if b is your length of base that you chose for your straw
And c is your length for the other side
And x is the third side's length.
c + x > b
So x > b - c
Don't forget to include units.
Example: My base is a straw that is 8 cm long. My side is 4 cm.
My third straw could be 6 cm or 5 cm and that would work to make a triangle.
If I made my straw 2 cm of 3 cm, it wouldn't work to make a triangle.
If my third side is x, then x > 8 - 4. Therefore x > 4 cm
The shortest possible third side to make a triangle would be 5 cm. (Or anything bigger than 4, example 4.1 cm) If you're just dealing with whole numbers (0,1,2,3,....), then 5 cm would be the shortest.)
The longest possible third side would be 11 cm. Try it with your straws if you made it 12 cm. It wouldn't work to make a triangle.

Answer 5

Inequality for shortest possible length: x > 4
Inequality for longest possible length: x < 12

Answer 6

would this one work? lengths 5 and 3 and lengths 6 and 4?

Answer 7

If your base is 8 cm, 5 and 3 wouldn't work to make a triangle. Try it and you'll see. 5 + 3 = 8 so if you flatten the two sides, they would look like a line on top of the base. It would be a line on top of a line. If you tried to open up the top and spread it, there would be a gap between the 5 cm piece and the 3 cm piece. A gap means it's wouldn't be a closed figure. A triangle can't have gaps.
If your base is 8 cm, then 6 and 4 would work.

Answer 8

So you're making the triangle with and 8 cm base, a side of 6 cm and a third side of 4 cm.

Answer 9

ok and this is the last thing ad ill leave you alone here is what i filled out on the sheet:
Straw Lengths 8 cm and 4 cm 6 cm and 4 cm

Possible lenghts
for a third side 6 cm or 5 cm 5 cm or 4 cm

Impossible lengths
for a third side 12 cm or 13 cm 11 cm or 10 cm

Inequality for third
side of length x x > 4 x > 6

would this be correct?

Answer 10

I think you need to say that x>4 and x<12 for the inequality for the first one.
Another way to write that is 4<x<12.

Then for the second set of numbers x>6 is not right. Since your base is 6 and your side is 4 cm, x + 4 > 6 therefore x > 2
You need to put that 2<x<10
For possible sides that don't work, you put correct numbers. But the numbers you chose are the 'too big' numbers. I just want you to keep in mind that there are also 'too small' numbers.

Answer 11

When you have time, try to use straw lengths to experiment. You'll be able to picture it better and it might make more sense.

Answer 12

thanks so much, you saved me!!! :)

Answer 13

oh also i took your advice before and i changed the numbers to 8cm for the base and 6cm for the side, sorry

Answer 14

so the last inequality would be 6 < x < 11?

Answer 15

You did two sets of numbers. 8 and 4 and then 6 and 4. Did they ask you to do the whole assignment twice? I'm just wondering.
If you just do what they are asking, I think they want you to do it once.
So you picked 8 cm as the base and 6 cm as one side.
Straw length = 8 cm
Side length = 6 cm
Two possible lengths (as the third side) that COULD be used to make a triangle are 6 cm and 4 cm.
Two lengths for the third side that would not make a triangle are 2 cm and 15 cm.
third side = x
x + 6 > 8 AND x < 6 + 8
so x > 2 AND x < 14
which can be combined as 2<x<14.
So the third side can be any number between 2 and 14 (not including 2 and 14) in order to make a triangle.

Answer 16

yeah there is activity 1 and activity 2 you just do it again

Answer 17

Oh okay. So you are using a base of 8 and a side of 6 cm for the first one.
What two lengths are you using for activity 2?

Answer 18

im using 8 and 6 for the 2nd one and for the first im using 8 and 4.

Answer 19

the one thing i need to understand is how do you find the shortest side and the longest side you can use for the 3rd?