Question

Периметр Ромба 72 см ,острый угол равен 60 Найти длину диагонали BD

Answer 1

AB=BC=CD=DA= 72:4=18 см
А= 60:2=30° , зная что угол который лежит напротив угла в 30° равен половине гипотенузы ,от цюда ВО = 1/2 АВ = 9 см
ВО+ОD=BD = 9*2 =18 cm

Answer 2

Perimeter of a Rhombus

To find the length of diagonal BD in a rhombus with a perimeter of 72 cm and an acute angle of 60 degrees, we can use the properties of a rhombus.

A rhombus is a quadrilateral with all sides of equal length. The diagonals of a rhombus bisect each other at right angles. Let's denote the length of the side of the rhombus as "s" and the length of the diagonal BD as "d".

Finding the Length of the Diagonal BD

To find the length of diagonal BD, we can use the formula for the perimeter of a rhombus and the properties of a rhombus.

The perimeter of a rhombus is given by the formula:

Perimeter = 4s

Given that the perimeter of the rhombus is 72 cm, we can set up the equation:

4s = 72

Simplifying the equation, we find that the length of each side of the rhombus is:

s = 72 / 4 = 18 cm Now, let's use the properties of a rhombus to find the length of diagonal BD.

In a rhombus, the diagonals bisect each other at right angles. This means that the angle between diagonal BD and side AB is 90 degrees.

Since we know that one of the acute angles of the rhombus is 60 degrees, we can use trigonometry to find the length of diagonal BD.

In a right triangle with one angle of 60 degrees, the sides are in a ratio of 1:√3:2. The side opposite the 60-degree angle is √3 times the length of the shorter side.

Let's denote the length of side AB as "a" and the length of diagonal BD as "d". We can set up the following equation:

a = s = 18 cm

d = a * √3 = 18 * √3 cm ≈ 31.18 cm Therefore, the length of diagonal BD in the rhombus is approximately 31.18 cm.

Please note that the calculations are approximate due to rounding.

I hope this helps! Let me know if you have any further questions.