Question

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 1

D

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:

`7+15>x`

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

`7+x>15`

Let's solve for x for both inequalities.

First inequality:

`7+15>x`

Add:

`22>x`

Flip:

`x<22`

Second inequality:

`7+x>15`

Subtract 7 from both sides:

`x>8`

So, we have the compound inequality:

`x>8\text{ and } x<22`

Combine:

`8<x<22`

Our answer is D

And we're done!