Question

Confused! Please explain!

one side of a triangle has a length of 6in and another side has a length of 3in. Which is the greatest possible value for the length of the third side?

I know there has to be an inequality because its Triangle Inequality Theorem.

Answer 1

the third side needs to be less than \(\large 6 + 3\)

Answer 2

otherwise the two sides will not be able to join the third side

Answer 3

in general, if \(a\) , \(b\) and \(c\) are sides of a triangle, they must satisfy :

\(\large c < a + b \)
\(\large a < b + c \)
\(\large b < c + a \)

Answer 4

in short : "sum of any two sides" must always be greater than the "third side"

Answer 5

The third side must be:
3 < third side < 9
When 2 sides are known the third side must be less than the sum of the other 2 sides and longer than the difference of the other 2 sides.

Answer 6

how do I solve?

Answer 7

How do you solve for the side 6 and 3 problem?

Answer 8

Since you know the two sides, just add them.
that gives the upper bound of possible third side

Answer 9

\(\large 3 + 6 = 9\)

so \(\large 9\) is the upper bound for third side

Answer 10

So the answer is 9? I just add them? no inequality or equation?

What about if a question like this comes up on a test (I have state testing tomorrow so im studying) then I just add the two sides??

Answer 11

Notice that the third side cannot equal \(\large 9\) however, It just needs to be less than \(\large 9\)

Answer 12

yes, you got it !

Answer 13

yes adding the two sides gives u the upper bound on third side

Answer 14

similarly, subtracting the two sides gives u the lower bound on third side

Answer 15

wish you good luck wid the exam :)