Question

A rectangle has a length of 8 inches. The area of the rectangle, in square inches, is an irrational number. The width of the rectangle must be ____

Answer 1

Answer: The width must be irrational

If you multiply a rational and irrational number together, the result is irrational. The length 8 is rational. The area is told to be irrational. This forces the width to be irrational. If the width were rational, then

rational*rational = rational

but the area was irrational. So this is a contradiction.

Answer 2

Width of rectangle must be an irrational number.

Explanation:

we know that,

Area of rectangle = Length * width

Length of rectangle is 8 inches ( a rational number)

Area of rectangle is an irrational number.

That means product of length and width of rectangle must be an irrational number.

Since here length of rectangle is a rational number then width of rectangle must be irrational in order to get area as an irrational number.