Need up to 30 seconds to load.

the triangle inequality theorem tells us

is that if you have you know three sides

that make up the sides of a triangle if

you add any two sides together they have

to add up to more than the third side if

they don't what you end up having is a

situation like this I kind of think of

it as a drawbridge but if these two

sides right here don't add up to the

length of this third side you can see a

triangle won't be formed because they

can't span that distance they can't

reach it's almost like even if you

rotate these sides down there they're

stretching but they can't span that

distance right so any two sides added

together have to be more than the third

side okay so that's something that we're

paying attention to in this example now

when we have these two sides five and

twelve let's see if we can just sketch

it out just to give us a visual way of

appreciating this so here's 12 and let's

just say that here is five right so the

third side could be like like that right

but you see this point right here this

is like a hinge okay so if we take this

and we rotate it okay like this the most

extreme situation would be kind of like

this where this is 12 and this is like

five right here and then the third side

would have to span that distance like so

right so the longest aside here could be

would be up to 17 not including 17

because if it was equal to 17 this would

actually be laying completely flat there

would be no internal space that wouldn't

be a triangle now the other scenario is

if we were to take this side here and

rotate it down like this so that five is

like right here now it only has to span

this distance from here to here which is

only going to be seven units so

essentially if you think about it as a

as a hinge okay the most extreme example

is when you make it like a hundred and

seventy nine point nine degree angle or

you make it like a 0.1 degree angle

right so see they're folding this way or

it's folding like that

so essentially what we have here for

this third side we'll just call it X it

has to be greater than twelve minus five

and less than twelve plus five so that's

the shortcut if you want to just get

down to it just a simple way of doing

this you can write it as a compound

inequality and it's going to

somewhere in between the sum of the two

sides and the difference of the two

sides so if we simplify you can see X is

greater than seven and less than

seventeen not equal to because otherwise

then it's going to collapse on down flat

so that's how you would use a triangle

inequality theorem to solve for the

possible lengths of the third side again

the shortcut is just to add and subtract

the two side lengths and that'll give

you an interval of the possible lengths

of the third side so I hope this helped

clear that up for you subscribe to the

channel check out more math tutoring

videos on my youtube channel Mario's

math tutoring and I look forward to

seeing the future videos