# Find the side of the rhombus whose area is 120 cm2 and one of the diagonals is 24 cm.

The area of a rhombus is equal to half the product of the diagonals of the given rhombus. Let x centimeters be the length of the unknown diagonal of the rhombus, then the area of this rhombus is 120 = 24x / 2 = 12x, whence x = 10, so the length of the unknown diagonal of the rhombus is 10 centimeters. The diagonals of the rhombus intersect and the intersection point is divided in half, then consider the triangle AOB (see figure), the lengths of its sides are equal to half the lengths of the diagonals, i.e. are equal to 10/2 = 5 centimeters and 24/2 = 12 centimeters, then we can find the AB side by the Pythagorean theorem: AB ^ 2 = 5 ^ 2 + 12 ^ 2 = 25 + 144 = 169, whence AB = √169 = 13 centimeters, side AB of triangle AOB is also the desired side of the rhombus.

Answer: 13 centimeters.