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

The diagonals of the rhombus intersect at right angles and are halved at the intersection line. We have a right-angled triangle, the legs of which are half of the diagonals, the hypotenuse is the side of the rhombus. The square of the hypotenuse is equal to the sum of the squares of the legs, which means that the square of the side of the rhombus can be found as the sum of the squares of the halves of the diagonals.

a ^ 2 = (d1 / 2) ^ 2 + (d2 / 2) ^ 2 = (14/2) ^ 2 + (48/2) ^ 2 = 7 ^ 2 + 24 ^ 2 = 49 + 576 = 625 = 252;

a = 25 cm – rhombus side.

The perimeter of a rhombus is equal to the sum of the lengths of its sides, all sides of the rhombus are equal, which means:

P = 4 * a = 4 * 25 = 100 cm.