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Given the lengths of two sides of a triangle, find the range for the length of the third side (between what two numbers should the length of the third side be). Write the inequalities for each case. 8 and 13

Respuesta :

Answer:

5 < third side < 21

Step-by-step explanation:

Let the length of the third side be [tex]x[/tex].

We know that [tex]x[/tex] must be smaller than the sum of the lengths of the two other sides. Thus [tex]x < 21[/tex].

We also know that

[tex]x+8 > 13\\x > 5[/tex]

And

[tex]x+13 > 8\\x > -5[/tex]

So, in conclusion, [tex]5 < x < 21[/tex].

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