The diagonals of the rhombus are 14 cm and 48 cm. Find the side of the rhombus.

Let us denote the side of the rhombus by x, and the diagonals of the rhombus by y1 (y1 = 14 cm) and y2 (y2 = 48 cm). We calculate the length of the rhombus side (all sides of the rhombus are equal), taking into account that the sum of the squares of the diagonals of the rhombus is equal to the square of the rhombus side multiplied by a factor of 4.

y1 ^ 2 + y2 ^ 2 = 4x ^ 2.

14 ^ 2 + 48 ^ 2 = 4x ^ 2.

x ^ 2 = (14 ^ 2 + 48 ^ 2) / 4.

x = √ ((14 ^ 2 + 48 ^ 2) / 4) = √ ((196 + 2304) / 4) = √ (2500/4) = √625 = 25 cm.

Answer: The length of the side of the rhombus is 25 cm.