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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