Aballroom 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? choose each statement that is true about the new dance floor. a. the area of the floor would be a rational number. b. the area of the floor would be an irrational number. c. each side length would be a perfect square. d. the area of the floor would be a perfect square. e. the area of the floor would be a nonterminating, nonrepeating decimal

It is given in the qustion that

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

And the formula of area of square is side square.

So we will get

Taking square root on both sides,

And on increasing the side length by one foot , we will get side length of 21 feet .

And it is not a perfect square .

And the area is

And 441 is a perfect square and a rational number .

Therefore true statements are A and E .

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for

what level of math? also i don't need to be paid if i can you.