Question

12. Which of the following lengths could be the sides of a triangle?

A. 6 cm, 18 cm, 12 cm

B. 15 cm, 22 cm, 8 cm

C. 22 cm, 13 cm, 8 cm

D. 18 cm, 6 cm, 12 cm
@AccessDenied

Answer 1

no its not

Answer 2

We should use the triangle inequality idea, which in its most basic form says that the three sides are not too out of proportion that two segments are the same length as the third nor are they too short to even create the triangle.


The triangle inequality states that with the sides of the triangle length a, b, c, then all of the following are TRUE:
a + b > c, a + c > b, and b + c > a

Answer 3

So for an example:
. A. 6 cm, 18 cm, 12 cm
Let's call a=6 cm, b = 18 cm, and c = 12 cm
Then:
a + b > c
6 + 18 > 12 This looks true
a + c > b
6 + 12 > 18
18 > 18 That ISN'T true! They' re equal! So this means our figure is actually just a line segment.

Answer 4

so would my answer be B?

Answer 5

I think (B) looks good. :)
15+22 > 8 is obviously true
15+8 > 22
23 > 22 That is true,
8+22 > 15 That is also true! It works!

Answer 6

thanks, can you help me on some and check my answers on the ones i already did?

Answer 7

Sure, just post them. :)

Answer 8

I thought it was (a^2) + (b^2) = (c^2) for a triangle
C = the biggest number

Answer 9

a^2 + b^2 = c^2 applies only for right triangles, where c is your hypotenuse.

Answer 10

can you check if those are right?

Answer 11

Observing that #1 just means to look for the corresponding parts, CE and NP do correspond in the written names. So that checks out.
#2 we know two sides are congruent as given. And we know they share a side as well. So that would give us all three sides congruent, SSS checks out.

Answer 12

Where do you find that the other two sides are congruent for SSS? We don't have any information about those, only the one side at the edge.

Answer 13

so it would be D?

Answer 14

Not quite... we do have information to work with, just not about the sides.
BC and EF are parallel and you have two large transversals going between their endpoints (BF and CE), so perhaps there is information you can find on the angles that is useful with the congruence of BC and EF.

Answer 15

so then it would be SAS, correct?

Answer 16

We don't have two sides, but we have two angles and their included side.