# TSI Math: Understanding the Properties of a Triangle

Two sides of a triangle are known. These two sides measure 13 and 18 units. Which of the following could NOT be the perimeter of the triangle?

Geometry and Measurement | Measurement (Linear, Area, Three-Dimensional) |

Mathematics and Statistics Assessment | Measurement (Linear, Area, Three-Dimensional) |

Product Type | TSI |

TSI | Mathematics and Statistics Assessment TSI Math TSI Mathematics |

TSI Math | Geometry and Measurement |

TSI Mathematics | Geometry and Measurement |

Test Prep | TSI |

### Transcript

here and it's connected here and there's Another one's eighteen

so hung time take out the triangle inequality serum We

aren't given the length of the third side of the

triangle but using that to given sides allows us to

find a range of possible lengths for the third leg

The triangle inequality Throughem tells us that given to sides

they envy of the triangle is less than be the

third side Must be between b minus a and b

plus eh Right So well see why this is true

Imagine the angle between a and b is very small

In that case vienna are almost on top of each

other Almost looks like a thick line The third side

that connects them can't be shorter than be minus a

well The other extreme All the angle between a and

b is very large Say close to one hundred eighty

degrees and if that's the case then the third side

that connects them can't be longer than b plus eh

So we have two sides of the triangle and we

know the third side must have a length Between well

eighteen minus thirteen is five units or well eighteen plus

thirteen is thirty one units Interesting So if the third

side fell out of this range we would not be

able to connect the three sides to actually make a

triangle It'd be other too short or too long Well

given that the third side must measure between five and

thirty one units the perimeter of the entire triangle must

be between thirteen plus eighteen plus five that's thirty six

units and sixty two units We have thirteen plus eighteen

thirty one right well the only answer choice that lives

outside this ranges eh thirty five units So that's the 00:01:50.536 --> [endTime] answer for shmoop