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?

We determine the third side of a triangle if we are given certain measurements or parameters like two sides and an angle, two angles and one side or two sides and the type of triangle. For this case, we are only given the measurement of the two sides of the triangle. In order to solve the third side, we assume that the triangle is a right triangle where one angle is a right angle. From this assumption, we use the Pythagorean Theorem:

c^2 = a^2 + b^2 where c is the hypotenuse, a and b are the remaining sides of the triangle

From this assumption, we can already calculate the third side by either assuming that 15 in. is the hypotenuse or to assume the two to be the shorter sides of the triangle. By assuming 15 in. to be the hypotenuse, we obtain a measurement of the third side a value of 10.20 in. while assuming the latter we obtain a value of 18.60 in. From the claim of Aziza, she is correct when she said that the third side is greater than 4 in. however she is wrong in claiming that the third side can have any length since a triangle has always its corresponding parameters depending on what type it is or the measurements being given in the problem. For this case, the third side can be 18.60 in. or 10.20 in.