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15 August, 01:23

An acute triangle had two sides measuring 8cm and 10 cm what is the best representation of the possible range of values for tge third side, s?

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  1. 15 August, 04:24
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    The third side must be >2 and < 18

    To test if a triangle is acute, right or obtuse:

    1) Square all 3 sides

    2) Sum the squares of the 2 shortest sides

    3) Compare this sum to side 3 squared

    if sum > side 3 squared it is an acute triangle

    if sum = side 3 squared it is a right triangle

    if sum < side 3 squared it is an obtuse triangle

    The shortest side 2 can be is "less than 2" so we'll say it is 2.00000001

    three sides squared =

    4.00000004

    64

    100

    Summing the 2 shortest sides 4.00000004 + 64 = 68.00000004

    68.00000004 is less than 100 so it is an obtuse triangle no matter how long the third side is.
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