Can a triangle have side measurements of 1, 4 and 5? Why or why not

A triangle cannot have side measurements of 1, 4 and 5.

As the sum of two sides i. e. '1+4' of a triangle is not greater than the measure of the third side i. e. '5'.

Step-by-step explanation:

The Triangle Inequality Theorem states that the sum of any two sides of a triangle must be greater than the measure of the third side.

For example, a triangle ΔABC must follow the three conditions which are as follows:

A + B > C B + C > A A + C > B

For example, a triangle ΔABC with side lengths:

A = 1

B = 4

C = 5

A + B > C → 1 + 4 > 5 (FALSE) B + C > A → 4 + 5 > 1 (TRUE) A + C > B → 1 + 5 > 4 (TRUE)

As the condition i. e. A + B > C → 1 + 4 > 5 is not satisfied, as 1 + 4 > 5 is False.

Therefore, a triangle cannot have side measurements of 1, 4 and 5.