Question

Do the side lengths 4, 5, and 10 form a triangle? Select the correct answer and reasoning.

Answer 1

Answer:

No, because 5 + 4 isn't greater than 10.

Step-by-step explanation:

Given

$Side\ 1 = 4$

$Side\ 2 = 5$

$Side\ 3 = 10$

Required

Do they form a triangle

To check if they form a triangle or not, we make use of trinagle inequality theorem which states that; for sides a, b and c

$a + b > c$

$a + c > b$

$b + c > a$

So for sides 4, 5 and 10, we have:

$4 + 5 > 10$ --- False

$4 + 10 > 5$

$5 + 10 > 4$

Since the one of the inequalities is false, then the sides do not form a triangle.