# geomerty

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two sides of a triangle have lengths 45 inches and 50 inches. How long can the third side be?

• geomerty -

any side must be less than the sum of the other two sides.

So, it must be less than 95.

• geomerty -

I could be any number between 5 and 95 inches

let it be x
x+ 45 >50 ---> x > 5
x+50 > 45 -- x > -5
50 + 45 > x
x < 95

so x > -5 and x > 5 and x < 95
so 5 < x < 95

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