Question

Aziza has a triangle with two sides measuring 11 in. and 15 in. She claims that the third side can be any length as long as it is greater than 4 in. Which statement about Aziza’s claim is correct?

Answer 1

Answer:

Aziza’s claim is incomplete. The third side must be between 4 in. and 26 in.

Step-by-step explanation:

With the Triangle Inequality Theorem, saying that the sum of lengths of any two sides of a triangle is greater than the length of the third side. With this we can develop two inequalities:

11 + 15 > x

26 > x

rewrite this as x < 26

11 + x > 15

x > 15 - 11   Subtract 11 from both sides

x > 4

Therefore, the third side can be anywhere greater than 4 inches and less than and less than 26 inches.

4 <  x < 26