Question

In the triangle KLM, KL = 14 and LM = 32. Which is a true conclusion?
Answer KM − KL > 2(32)
KL − KM > 32
LM + KL < 32
KM − LM < 14

Answer 1

can sumbody help me please

Answer 2

none. I think.

Answer 3

The Triangle Inequality is useful for this problem. Basically it says that the lengths of the two shortest sides of the triangle must be greater than the longest side of the triangle.

Answer 4

it has 2 b one of those

Answer 5

d is probably correct

Answer 6

Hint: (to help eliminate at least one of the choices)

Suppose KL and LM are the SHORTEST sides of the triangle. Then, by the triangle inequality, when you add KL and LM it should be LONGER than the third side.

Answer 7

bcoz difference of 2 sides of triangle is greater than the 3rd side

Answer 8

You mean the SUM of 2 sides is greater that the 3rd side

Answer 9

x+y > z
implies
z-x<y

Answer 10

here x,y,z are sides of tiangle

Answer 11

Also, in your example Sriram, z is the LARGEST side.

so x + y > z
or
z - y < x
or
z - x < y

Again, if z is the LARGEST side.

Answer 12

nope it is true for all sides
try it wid any of the sides u will get the same result

Answer 13

Bottom line: the answer is not in the given

Answer 14

Oh my god. :(

I am sleepy.

Of course it works this way. If z is the smallest side, it is , BY DEFAULT smaller than either of the other two, and of course smaller than their sum.

Oh dear.

Answer 15

the answer is d!!
given above

Answer 16

What do you mean by d?

Answer 17

Assume he means KM − LM < 14...

Answer 18

Ok, I must redeem myself, so here we go. :)
I originally mis-stated the triangle inequality. I stated a specific version, but the FULL version says "The sum of ANY TWO lengths of a triangle MUST BE greater than the third length."
Now, for this problem...

In the triangle KLM,
KL = 14
LM = 32
KM = unknown

The question is: which is a true conclusion?

KM − KL > 2(32)
This makes no sense. It's saying that KM > KL + 2(32). The third side of the triangle cannot be greater than the sum of the other two lengths.

KL − KM > 32
Again, this makes no sense. It's saying KL > 32 + KM. The third side of the triangle cannot be greater than the sum of the other two lengths.

LM + KL < 32
Once more, we have something which contradicts the triangle inequality. The sum of two sides must be greater than the other side or you don't have a triangle.

KM − LM < 14
This DOES make sense. It says KM < LM + 14 Which is to say, The sum of LM and 14 (or LM and KL) is GREATER Than the other side. This is the triangle inequality and this is correct. :)