Math

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emily is constructing a triangle one side is 3 inches long and another is 5 inches long which of the following is the smallest measure emily could use for the third side of the triangle

is it 2 inches? 3 inches? 4 inches? or 5 inches?

  • Math -

    any side of a triangle is less than the sum of the other two sides. So, if x is the missing side,

    5 < x+3
    2 < x

    so, x must be at least 2.

    Similarly, there is a maximum value for x, since we must also have

    x < 5+3
    x < 8

    since, even stretching out the other two sides end to end, they couldn't reach farther than 8.

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