The diagonal of rectangle is 36 meters long and makes an angle of 25° with one side of rectangle. Find the perimeter of the parallelogram.
the two sides have lengths
x = 36 cos25°
y = 36 sin25°
and the perimeter, as usual is
p = 2(x+y)
this is assuming it is a rectangle, and not just a parallelogram, where more information would be needed.
To find the perimeter of the parallelogram, we first need to find the length of the sides of the rectangle.
Let's assume the length of the rectangle is L and the width is W.
Given that the diagonal of the rectangle is 36 meters and makes an angle of 25° with one side of the rectangle, we can use trigonometry to find the length of the sides.
Using the sine function, we can write the equation:
sin(25°) = L / 36
To find L, we can rearrange the equation:
L = 36 * sin(25°)
We can use a scientific calculator or an online calculator to get the value of sin(25°) and calculate L.
Next, we can use the Pythagorean theorem to find the width of the rectangle:
W = √(36^2 - L^2)
Now that we have the length (L) and width (W) of the rectangle, we can find the perimeter of the parallelogram.
Perimeter = 2 * (L + W)
Plug in the values of L and W that we obtained from the previous calculations to calculate the perimeter.