if we increased one side of a square by 5 units and decreased the other by 3 units the area of the resulting rectangle would be 21 units squared greater than the area of the square how long are the sides of the original square

18 units

Step-by-step explanation:

So let's list out the sides.

for the first square let's just call them x

for the second square then they would be x+5 and x-3

So let's write out their areas we will cal the area of the first one z

x*x = z

(x+5) * (x-3) = z+21

since z = x^2 we can set up the second equation as a quadratic.

(x+5) * (x-3) = x^2 + 21

x^2 - 3x + 5x - 15 = x^2 + 21

But look, the x^2s cancel out

2x - 15 = 21

2x = 36

x = 18

Test it out and see if it fits the description, And if you don't understand anything just let me know so I can explain more.