The area of a square is 400 square units. Select all the statements that would be true if the length of each side of the square increased by one unit. A-The area of the square would be a rational number.
B-The area of the square would be an irrational number
C-Each side length would be a perfect square.
D-The area of the square would be a perfect square. d
E -The area of the square would be a nonterminating, nonrepeating decimal.
PLEASE ANSWER ASAP WILL GIVE BRAINLIEST!

A and D

Step-by-step explanation:

Given that the area of a square = 400 units² = s²

Where s is one side length of the square.

It means that the side length (s) = √400 = 20

If the length of each side length increase by 1 units, new side length = 21 units

Area of new square = 21² = 441

The following statements would be true if the side length was increased by 1 units:

A. "The area of the square would be a rational number"

441 is a rational number, because a rational number is a quotient of two integers.

441 and 1 are two integers. Their quotient = 441. I.e. 441 ÷ 1 = 441

D. "The area of the square would be a perfect square".

A number is considered a perfect square if it can be expressed as a product of two equal integers.

441 can be expressed as 21*21

(b) 240

step-by-step explanation:

first, we use the pythagorean formula using the given side lengths to find x. then we use x to find the side lengths. then we add the side lengths to find the perimeter.

pythagorean theorem formula:

a^2 + b^2 = c^2

(x - 20)^2 + (x - 40)^2 = x^2

x^2 - 40x + 400 + x^2 - 80x + 1600 = x^2

x^2 -120x + 2000 = 0

(x - 100)(x - 20) = 0

x - 100 = 0 or x - 20 = 0

x = 100 or x = 20

we see that the solution x = 20 must be discarded because it will give a negative side length and a side length of 0. the only valid solution is x = 100.

perimeter = sum of the lengths of the sides

perimeter = x + x - 20 + x - 40

perimeter = 3x - 60

replace x with 100.

perimeter = 3(100) - 60

perimeter = 300 - 60

perimeter = 240