MATH SOLVE

4 months ago

Q:
# Raj made this argument: The Triangle Inequality Theorem states that if the lengths of three sides of a triangle are a, b, and c, then a + b > c. For this reason, since a, b, and c are all positive numbers, the square of a + b must be greater than the square of c. However, for a right triangle, the Pythagorean Theorem states that if the lengths of the legs are a and b, and if the length of the hypotenuse is c, then a2 + b2 = c2, not a2 + b2 > c2. Therefore, since the Pythagorean Theorem is known to be correct, and since right triangles should adhere to the Triangle Inequality Theorem, the Triangle Inequality Theorem must be incorrect. What is wrong with Raj’s argument?A) The square of a + b is not equal to a2 + b2. B) One cannot assume that a, b, and c are all positive numbers. C) It’s not true that right triangles should adhere to the Triangle Inequality Theorem. D) It’s not true that according to the Triangle Inequality Theorem, a + b > c.

Accepted Solution

A:

Selection A is appropriate.

_____

(a +b)^2 = a^2 +b^2 +2ab, so is greater than a^2 +b^2 for a > 0, b > 0.

_____

(a +b)^2 = a^2 +b^2 +2ab, so is greater than a^2 +b^2 for a > 0, b > 0.