Question

A city park, shaped like a square, has an area of 2 square miles. The city manager wishes to calculate the perimeter of the park. Which is the correct perimeter, and is this value rational or irrational?

a) 4√2 miles, and this value is irrational
b) 4√2 miles, and this value is rational
c) 2√2 miles, and this value is irrational
d) 2√2 miles, and this value is rational

Answer 1

The area of the park is 2 square miles. The perimeter of the park is 4√2 miles, and this value is rational.

Step-by-step explanation:

The area of a square is given by the formula A = s^2, where s is the length of one side of the square. In this case, the area is given as 2 square miles. Therefore, 2 = s^2. Solving for s, we find that s = √2.

The perimeter of a square is given by the formula P = 4s, where s is the length of one side of the square. Substituting the value of s, we get P = 4(√2) = 4√2 miles.

Since the value 4√2 can be expressed as a simple fraction (4/1) and is not an infinite decimal, it is a rational number. Therefore, the correct perimeter of the park is 4√2 miles and this value is rational.

The correct answer is d) 4√2 miles, and this value is rational.