# Geometry

If two sides of a triangle are 12 cm and 20 cm, the third side must be larger than ________ cm and smaller than ________ cm.

Fill in the blank and explain, please and thank you!

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1. Property of any triangle:
The sum of any two sides of the triangle must be greater than the third side.

so
1. x+12>20 or x > 8
2. 12+20 > x or x < 32
3. x+20 > 12 or x > -8 , well that's obvious

so it looks like 8 < x < 32

check: let x=10
is 10+12 > 20 yes
is 10+20 > 12 yes
is 20+10 > 12 yes

check: let x = 5 (outside our domain)
is 5+10 > 20 NO!

check: let x = 40 (outside our domain on the other side)

is 10+12 > 40 NO.

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posted by Reiny

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