Question

A ballroom has a square dance floor. The area of the floor is 400 square feet. If the length of each side of the square increased by one foot, would its area be a rational number? explain

Answer 1

Yes, in the sense that the new area could be written as (x+1)^2  /   1.
Usually we would not bother with the "1" as divisor.

Let's actually do the work:  what is the area of the square if we increase the side length of the existing square by 1 ft?

(x+1)^2 = x^2 + 2x + 1        (This is not a fraction, and thus not the ratio of
                                            two integers, which, in turn, is the definition of
                                            "rational number."

Answer 2

Answer:

The area is a rational number.

Step-by-step explanation:

Consider the provided information.

A ballroom has a square dance floor. The area of the floor is 400 square feet.

Area of square = (side)²

Substitute the respective value in above formula.

400 = (side)²

√400 = side

20 feet = side

Ignore the negative value as side cannot be a negative number.

Now it is given that the length of each side of the square increased by one foot,

Thus, the new side is 20 + 1 = 21 feet

Now find the area of new square = (side)²

A = 21²

A = 21×21

A = 441 square feet

The number 441 is a rational number.

Hence, the area is a rational number.