# The perimeter of the rhombus is 68 cm and the length of the diagonal is 30 cm find the second diagonal

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

The perimeter of a rhombus is the sum of all its sides.

P = AB + BC + CD + AD.

Since all sides of the rhombus are of the same length, and the perimeter is 68, then:

AB = BC = CD = AD = P / 4;

AB = BC = CD = AD = 68/4 = 17 cm.

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

AO = OS = AC / 2;

AO = OS = 30/2 = 15 cm;

BO = OD = BD / 2.

To calculate the diagonal BD, we calculate the length of the segment BO. To do this, consider the triangle ΔABO, which is rectangular.

Let’s apply the Pythagorean theorem:

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

BО ^ 2 = AB ^ 2 – AO ^ 2;

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

BО = √64 = 8 cm.

BD = BO · 2;

ВD = 8 2 = 16 cm.

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