Is it possible to construct a triangle with sides 4,5,9? If not, explain why.

To have a triangle, the sum of any two sides must be greater than the third side, so check:

4+5 > 9
NO
Therefore , no triangle is possible

To determine whether it is possible to construct a triangle with sides measuring 4, 5, and 9, we can use the Triangle Inequality Theorem.

According to the Triangle Inequality Theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. In other words:

a + b > c
b + c > a
c + a > b

Let's apply this theorem to the given sides: 4, 5, and 9.

4 + 5 > 9 (9 > 9). This inequality is true.
5 + 9 > 4 (14 > 4). This inequality is true.
9 + 4 > 5 (13 > 5). This inequality is true.

Since all three inequalities are true, we can determine that it is possible to construct a triangle with sides measuring 4, 5, and 9.

Therefore, the answer to the question is "Yes, it is possible to construct a triangle with sides 4, 5, and 9."