The side of the square was enlarged 5 times and a new square was obtained, the area of which is 384

The side of the square was enlarged 5 times and a new square was obtained, the area of which is 384 cm2 larger than this square. Find the side of the given square?

1. Let the original side of the square be y. Then its area of the given square is equal to y2. The side of the new square is 5y. In this case, the area of the new square is equal to y2 + 384 or (5y) 2. Let’s compose an equation where we equate the values of the area of the new square:

y ^ 2 + 384 = (5y) ^ 2,

y ^ 2 + 384 = 25y ^ 2,

384 = 25y ^ 2 – y ^ 2,

384 = 24y ^ 2,

y ^ 2 = 384/24,

y ^ 2 = 16,

y = √16,

y = 4 cm.

Answer: the side of this square was 4 cm.