Question

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?

Answer 1

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.