Question

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

Question 5 options:

A)

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

B)

Yes, because each side length is less than 15.

C)

Yes, because the sum of the side lengths is 19.

D)

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

Answer 1

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

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.