Question

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

Answer 1

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'.

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.