Since the given triangle is a right triangle, we can apply the Pythagorean Theorem to write: a² + b² = c²
This means we can take Quantity B and replace c² with a² + b² to get:
QUANTITY A: (a + b)²
QUANTITY B: a² + b²

Expand and simplify Quantity A to get:
QUANTITY A: a² + 2ab + b²
QUANTITY B: a² + b²

Subtract a² and b² from both quantities to get:
QUANTITY A: 2ab
QUANTITY B: 0

Since it must be the case that a > 0 and b > 0, we can see that Quantity A is greater.

Answer: A