Find the second diagonal of the rhombus, the side of which is 17 cm and one of the diagonals is 30 cm.

A rhombus is called a parallelogram in which all sides are equal.

The diagonals of the rhombus intersect at right angles and the intersection point is halved:

AO = OC = AC / 2;

AO = OC = 30/2 = 15 cm;

ВO = OD = ВD / 2.

Therefore, in order to find the length of the ВD diagonal, it is necessary to calculate the length of the AO segment.

To calculate the length of the ВO segment, consider the triangle ΔABO. This triangle is rectangular, since the diagonals intersect at right angles.

Let’s use the Pythagorean theorem. According to this theorem, the hypotenuse squared is equal to the sum of the squares of the legs:

AB ^ 2 = BO ^ 2 + AO ^ 2;

BO ^ 2 = AB ^ 2 – AO ^ 2;

ВO ^ 2 = 17 ^ 2 – 15 ^ 2 = 289 – 225 = 64;

ВO = √64 = 8 cm.

ВD = ВO · 2;

ВD = 8 2 = 16 cm.

Answer: the length of the ВD diagonal is 16 cm.