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?

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.

To determine the smallest possible measure for the third side of the triangle, we can use the triangle inequality theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

In this case, we already know that one side of the triangle is 3 inches long and another side is 5 inches long.

To find the smallest possible measure for the third side, we need to find the difference between the lengths of the other two sides:

5 inches - 3 inches = 2 inches

Therefore, the smallest measure Emily could use for the third side of the triangle is 2 inches.