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TSI Math: Understanding the Properties of a Triangle 4 Views
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Description:
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?
Transcript
- 00:03
All right machin uppers Here we go Another question Foreign
- 00:05
triangle's Two sides of a triangle are known These two
- 00:09
sides measure thirteen and eighteen units Which of the following
- 00:12
could not be the perimeter of the triangle So let's
- 00:19
think about it But we have a line thirteen long
Full Transcript
- 00:21
here and it's connected here and there's Another one's eighteen
- 00:24
so hung time take out the triangle inequality serum We
- 00:27
aren't given the length of the third side of the
- 00:28
triangle but using that to given sides allows us to
- 00:31
find a range of possible lengths for the third leg
- 00:34
The triangle inequality Throughem tells us that given to sides
- 00:38
they envy of the triangle is less than be the
- 00:40
third side Must be between b minus a and b
- 00:43
plus eh Right So well see why this is true
- 00:47
Imagine the angle between a and b is very small
- 00:49
In that case vienna are almost on top of each
- 00:52
other Almost looks like a thick line The third side
- 00:55
that connects them can't be shorter than be minus a
- 00:58
well The other extreme All the angle between a and
- 01:01
b is very large Say close to one hundred eighty
- 01:03
degrees and if that's the case then the third side
- 01:06
that connects them can't be longer than b plus eh
- 01:09
So we have two sides of the triangle and we
- 01:11
know the third side must have a length Between well
- 01:13
eighteen minus thirteen is five units or well eighteen plus
- 01:18
thirteen is thirty one units Interesting So if the third
- 01:23
side fell out of this range we would not be
- 01:25
able to connect the three sides to actually make a
- 01:28
triangle It'd be other too short or too long Well
- 01:31
given that the third side must measure between five and
- 01:33
thirty one units the perimeter of the entire triangle must
- 01:36
be between thirteen plus eighteen plus five that's thirty six
- 01:40
units and sixty two units We have thirteen plus eighteen
- 01:44
thirty one right well the only answer choice that lives
- 01:47
outside this ranges eh thirty five units So that's the 00:01:50.536 --> [endTime] answer for shmoop
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