Triangle Inequality Theorem
The triangle inequality theorem states that no two sides, when added, can be less then the length of the third side. However, that doesn't stop our brother from giving us two slices of cake that are definitely smaller than his slice. Not cool, bro.
|Triangles||Theorems About Triangles|
7 and x... ...while slice of pizza DEF has side lengths
of 8, 9 and y.
If x and y are integers, what is the largest possible value for x plus y?
Ok, here are the choices:
Right away we can throw "A" to the wolves. In all our days of pizza-eating...
...we've never seen a slice that exists in negative space.
Awesome - we have instantly increased our chances of getting this problem correct by
20%. According to the triangle inequality theorem...
...no side of a triangle can be longer than the sum of the other two sides.
Since we know this rule to be true... ...we know for a fact that the third side
of slice ABC has to be less than 12... ...and the third side of slice DEF has to
be less than 17. Since we're also told that x and y are integers,
or numbers that do not contain any fractions or decimal points after it...
...11 and 16 are the max values for sides x and y, respectively.
Add 'em together, and you get 27... which is choice "D."
Okay, Pisano -- fork it over. And put some pep in your step.