Jeremiah will not be able to create the triangular component with these toothpicks without modifying any of the lengths, according to the Triangle Inequality Theorem.
The Triangle Inequality Theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In other words:
a + b > c
b + c > a
a + c > b
where a, b, and c are the lengths of the sides of the triangle.
In this case, the toothpicks have lengths of 4 in., 5 in., and 1 in. If we assume that the 5 in. toothpick is the longest side (c), then we have:
a + b > c
4 in. + 1 in. > 5 in.
This inequality is not true, since 4 in. + 1 in. = 5 in., which is not greater than 5 in. Therefore, Jeremiah will not be able to create the triangular component with these toothpick lengths without modifying any of the lengths.
