Question

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

Answer 1

Area of a square = l x l

Area of a square = l^2

where l = length

From the question area of the square floor = 400 square feet

This implies that:

`400=l^2`

Take the square root of both-side

`\sqrt{400\text{ }}=√(l^2)`

20 = l

This implies each length of the dance floor is 20 feet

The question further state that the length of each side of the square dance floor is increases by one foot

This implies that the new length of each side of the square dance floor becomes 20 + 1 = 21

The new area of the square dance floor =

`l^2`

= l x l

= 21 x 21

= 441 square feet

There the area which is 441 square feet is a rationa number