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.
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