Question

Find the domain and range that represents the perimeter p of the triangle shown.

Options:
a. Domain: All real numbers, Range: All real numbers
b. Domain: Positive integers, Range: Positive integers
c. Domain: Non-negative integers, Range: Non-negative integers
d. Domain: Natural numbers, Range: Natural numbers

Answer 1

The domain and range for the perimeter of a triangle are all positive real numbers, allowing for any real number value for the sides and corresponding perimeter excluding zero and negative values.Option A is correct answer.

Step-by-step explanation:

The domain and range for the perimeter p of a triangle represenatation are the set of values the sides of the triangle can take and the corresponding set of perimeters, respectively. The length of the sides of a triangle must be positive to have a meaningful geometric figure, but they do not have to be integers. However, perimeter, as a measurable quantity, should also be a positive value but does not need to be an integer. Since we cannot have a triangle with sides of zero length (which would not enclose any area), the domain only includes positive real numbers, not zero or negative numbers. So, the correct answer to this question is option a. Domain: All real numbers, Range: All real numbers.