In any rhombus one angles is 60 and perimeter is 40 meter. Longer diagonal will be
Each of the sides must be 10 m
The longer diagonal creates an isosceles triangle with angles 30,30 and 120°
Several ways to do this
1. Construct a perpendicular which will bisect the diagonal.
Let the diagonal be 2x
then x/10 = cos30°
x = 10cos30 = 8.66..
2x = 17.32 m correct to 2 decimals
2. using the cosine law
d^2 = 10^2 + 10^2 - 2(10)(10)cos120
= 300
d = √300 = 17.32 m , same as above
reiny can you please help me with my post thanks
To find the longer diagonal of a rhombus, we can use the properties of a rhombus. A rhombus is a quadrilateral with all sides of equal length but opposite angles are equal as well.
We are given that one angle of the rhombus is 60 degrees. Since one angle is given, we can determine the other angles of the rhombus using the properties of a rhombus.
Since opposite angles of a rhombus are equal, we know that all four angles of the rhombus are equal to 60 degrees.
To find the lengths of the sides, we can use the formula for the perimeter of a rhombus. The perimeter is given as 40 meters.
Since a rhombus has four equal sides, we can divide the perimeter by 4 to find the length of each side:
Length of each side = Perimeter / 4 = 40 / 4 = 10 meters.
Now that we know the length of each side, we can find the longer diagonal.
The longer diagonal of a rhombus can be found using the formula:
Longer diagonal = 2 * square root of (side length^2 + side length^2).
In this case, the side length is given as 10 meters. Plugging in this value into the formula, we have:
Longer diagonal = 2 * square root of (10^2 + 10^2).
Simplifying further, we have:
Longer diagonal = 2 * square root of (200).
Using a calculator, we can evaluate the square root of 200 to be approximately 14.142.
Finally, we multiply this value by 2 to find the longer diagonal:
Longer diagonal = 2 * 14.142 = 28.284 meters.
Therefore, the longer diagonal of the rhombus is approximately 28.284 meters.