Question

The area of the square shown is 2 square centimeters.



Which of the following describes 4s, the perimeter of the square in centimeters?

A.
It is an irrational number, since s is rational, and 4 times a rational number is irrational.

B.
It is a rational number, since s is irrational, and 4 times an irrational number is rational.

C.
It is an irrational number, since s is irrational, and 4 times an irrational number is irrational.

D.
It is a rational number, since s is rational, and 4 times a rational number is rational.

Answer 1

Area = 2, so side length s = √2, which is irrational. The perimeter 4s = 4√2. If 4√2 were rational, then √2 = (4√2)/4 would be rational, a contradiction. Hence 4s is irrational. Answer: C.