Find the large diagonal of a rhombus if the side of the rhombus and its smaller diagonal are 5 meters

Find the large diagonal of a rhombus if the side of the rhombus and its smaller diagonal are 5 meters and 6 meters, respectively

It is known that the diagonals of a rhombus intersect at right angles and are halved at the point of intersection. Thus, the halves of the diagonals and the side of the rhombus form a right-angled triangle, in which the side of the rhombus a is the hypotenuse, the smaller leg is equal to half of the smaller diagonal d1, the larger leg is equal to half of the larger diagonal d2. By the Pythagorean theorem:

a ^ 2 = (d1 / 2) ^ 2 + (d2 / 2) ^ 2.

Hence:

(d2 / 2) ^ 2 = a ^ 2 – (d1 / 2) ^ 2 = 5 ^ 2 – (6/2) ^ 2 = 25 – 9 = 16;

d2 / 2 = √16 = 4.

The large diagonal of this rhombus is d2 = 4 * 2 = 8 cm.