# ACT Aspire Math: Which Side Length Could NOT Complete the Triangle?

###### Recommendation

### Want a study guide too?

A triangle has one side that's 6 units long and another side that's 5 units long.

Which of the following could not be the length of the third side?

ACT Aspire | Math |

ACT Aspire Math | Geometry |

Math | Geometry |

Product Type | ACT Aspire |

Test Prep | ACT Aspire ACT Aspire Math |

### Transcript

inequality serum Given any two sides of a triangle the

third side must be between the absolute difference of the

two sides and some of the two sides Well here's

another way to think about the problem Imagine you're a

giant gymnast with one leg that's five feet long and

another one that's six feet long Well when you're standing

up right with both legs together one of your legs

doesn't reach the ground Well the shorter leg finally manages

to reach the ground so that you form a triangle

with the ground The distance between your two feet can't

be any longer than the absolute difference of the two

sides so it has to be at least well one

foot there right So before that point your other leg

can't reach the ground so you could only make an

incomplete triangle with the ground Well once you reached one

hundred eighty degree split your no longer forming a triangle

with the ground at the very last point at which

you form a triangle with the ground while the distance

between your two feet will be no greater than the

sum of the length of your two legs Well in

this case one leg is six and the other is

five and the absolute difference of them is one So

the sum of the two sides is eleven The third

side can't be exactly one because well then the angle

between the two given sides would be zero degrees Well

the third side can't be eleven because this would require

the angle between the two given sides to be one

hundred eighty degrees And it's not really a triangle is

it Well the only answer choice that isn't between these 00:01:43.575 --> [endTime] two Numbers is 11 e yeah