Question

Which of the following possibilities will form a triangle?

Side = 16 cm, side = 8 cm, side = 7 cm
Side = 16 cm, side = 9 cm, side = 7 cm
Side = 17 cm, side = 12 cm, side = 7 cm
Side = 17 cm, side = 11 cm, side = 5 cm

Answer 1

I think this is C

Answer 2

@xiogonz

Answer 3

where is your work

Answer 4

how do you know without solving

Answer 5

@XioGonz

Answer 6

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Gucchi
I think this is C
\(\color{#0cbb34}{\text{End of Quote}}\)
You are Correct

Answer 7

Alright, Thanks!

Answer 8

@jimthompson5910 can you give an equation on how it is C?

Answer 9

C i think not sure tho

Answer 10

In order for a triangle to be possible, the sum of any two sides must be larger than the third side.

In choice A, we have side2+side3 = 8+7 = 15, but this is not larger than side1 = 16. So we rule out choice A.

In choice B, we have side2+side3 = 9+7 = 16, but this is also not larger than side1 = 16. We rule out choice B.

I'll skip over choice C and come back

In choice D, we have side2+side3 = 11+5 = 16 but that's not larger than side1 = 17. So we rule out choice D.

Answer 11

Wow, This is great! Thanks so much for this.

Answer 12

Now let's focus on choice C only

Let's say the three sides are x,y,z
x = 17
y = 12
z = 7

note how x+y = 17+12 = 29 which is larger than z = 7
Also, x+z = 17+7 = 24 which is larger than y = 12
Finally, y+z = 12+7 = 19 which is larger than x = 17

So if we pick any two sides of this triangle, add them up, then that sum will be larger than the third side we didn't pick on. This is one example of the triangle inequality theorem and shows why choice C is a possible triangle we can form.

Answer 13

I recommend cutting out slips of paper with the lengths mentioned. Try to physically form triangles based on those lengths. You should find that choices A,B, and D aren't possible triangles.

Answer 14

True.

Answer 15

Thank you.

Answer 16

No problem