Final answer:
The length of the side of a square with an area of 16 cm² (option a) is a rational number because it can be calculated as 4 cm, given the area of a square is side², and 4 is a rational number.
Step-by-step explanation:
To determine which of the following is a rational number, let's consider each option:
- a) The length of the side of a square with area of 16 cm². The area of a square is calculated as the side length squared (s²). Thus, the side of a square with an area of 16 cm² is 4 cm (since 4² = 16), which is a rational number.
- b) The length of the side of a square with an area of 5 cm². Finding the side length involves taking the square root of the area. The square root of 5 is an irrational number because it cannot be expressed as a fraction of two integers.
- c) A non-terminating decimal. Generally, non-terminating decimals without a repeating pattern are not rational numbers. Rational numbers are those that can be expressed as a fraction, where both the numerator and the denominator are integers and the denominator is non-zero.
- d) The square root of a negative number. This is an imaginary number, not a rational number. Rational numbers are always real numbers.
Therefore, option a is the correct answer, as it represents the length of the side of a square with an area of 16 cm², which can be calculated using the formula for the area of a square (Area = side²) and the result is a rational number.