Respuesta :
Answer:
8[tex]\sqrt{2}[/tex]
Step-by-step explanation:
64/4=16
so that is 16 on each side.
The diagonal of the rhombus create a right triangle.
We then use the Pythagorean theorem.
[tex]a^{2} +b^{2} =c^{2}[/tex]
[tex]16^{2} +16^{2} =c^{2}[/tex]
[tex]256+256=c^{2}[/tex]
[tex]512 =c^{2}[/tex]
[tex]\sqrt{512} =c[/tex]
8[tex]\sqrt{2}[/tex]
The length of the diagonals of a rhombus with perimeter of 64 and one of its angles as 120 degrees are 16 units and 27.71 units
Properties of a rhombus
- The diagonals are angle bisectors
- The 4 sides are congruent.
- The diagonal are perpendicular bisectors
Therefore,
perimeter = 4l
where
l = length
64 = 4l
l = 64 / 4
length = 16
One of its angle is 120°. Therefore, let's use the angle to find the length of the diagonal.
Using trigonometric ratio,
cos 60° = adjacent / hypotenuse
cos 60° = x / 16
x = 16 × cos 60
x = 8
2(x) = diagonal
diagonal = 16 units
The second diagonal length
sin 60° = opposite / hypotenuse
sin 60 = y / 16
y = 16 × sin 60
y = 13.8564064606
y = 13.85
Therefore,
diagonal = 2(13.85) = 27.71 units
learn more on rhombus here: https://brainly.com/question/11801642
