When the area of a square is increasing four times as fast as the diagonals, what is the length of a side of the square

Length of a side of a square = 2√2 units

Step-by-step explanation:

Let the length of a square is 'x' units.

Therefore, Area of the square A = (Side)²

                                                      = x² square units

And by Pythagoras theorem,

(Diagonal)²= (Side 1)² + (Side 2)²

                 = x² + x²

                 = 2x²

Diagonal 'p' = x√2 units

It is given in the question that area of the square is increasing four times as fast as the diagonals.

-------(1)

Similarly,

Now by placing the value of and in equation (1),

Since,

x = 2√2

Therefore, length of a side of the square is 2√2.