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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.

Respuesta :

MrRoyal

Answer:

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

Step-by-step explanation:

Given

[tex]Side\ 1 = 4[/tex]

[tex]Side\ 2 = 5[/tex]

[tex]Side\ 3 = 10[/tex]

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

[tex]a + b > c[/tex]

[tex]a + c > b[/tex]

[tex]b + c > a[/tex]

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

[tex]4 + 5 > 10[/tex] --- False

[tex]4 + 10 > 5[/tex]

[tex]5 + 10 > 4[/tex]

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

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