A rhombus of sides 20cm han an angled of 60degree,find the lenghts of its diagonals

Mathematics

1 answer:

EleoNora [17]3 years ago

7 0

Answer:

20 cm and 34.64 cm.

Step-by-step explanation:

Consider the triangle with vertex 60 degrees. The diagonal is perpendicular to the other diagonal , and it bisects the 60 degree angle.

So we have the relation cos 30 = x / 20 where x = 1/2 of the diagonal.

x = 20 cos 30

x = 17.32

And as the diagonals bisect each other this diagonal = 2*17.32 = 34.64 cm.

Similarly, the other diagonal = 2 * 20 cos 60 = 20 cm

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The perimeter of a triangle is 57 centimeters. The longest side is 3 centimeter(s) less than the sum of the other two sides. Tw

Setler79 [48]

Let's say x is longest side, y is shortest side and z is the other side. So we have some equations such that

$x+y+z=57$ (by the first sentence)

$x=(y+z) -3$ (by the second sentence)

$2y=x-15$ (by the third sentence)

By the second equation, we have $y+z=x+3$ and if we use it in the first equation, then $x+y+z=x+(x+3)=57$ . So $x=27$

Since $x=27$ , if we use it in the third equation the we have $2y=x-15=27-15=12$ then $y=6$

Therefore $z=24$

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3 years ago

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skelet666 [1.2K]

Answer: (99/13, 150/13)

Step-by-step explanation:

I'm too lazy to explain so here's a screen shot from desmos.