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Two sides of a triangle have lengths of 7 and 15. Which inequality represents the possible lengths for the third side?

A) 8 < x < 7
B) 7 < x <15
C) 8 < x < 15
D) 8 < x <22

Answer :

xKelvin

Answer:

D

Step-by-step explanation:

From the triangle inequality, we know that the two small sides must be greater than the largest side. Let's let x be the third side:

[tex]7+15>x[/tex]

However, 15 can also be our largest side. So:

[tex]7+x>15[/tex]

Let's solve for x for both inequalities.

First inequality:

[tex]7+15>x[/tex]

Add:

[tex]22>x[/tex]

Flip:

[tex]x<22[/tex]

Second inequality:

[tex]7+x>15[/tex]

Subtract 7 from both sides:

[tex]x>8[/tex]

So, we have the compound inequality:

[tex]x>8\text{ and } x<22[/tex]

Combine:

[tex]8<x<22[/tex]

Our answer is D

And we're done!

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