What is the perimeter of rectangle
MNOP , rounded to the nearest tenth of a meter?
A picture of the rectangle MNOP. MO is diagonal. The length of MO is 28 m. The angle of M is 60 degrees, and O is 30 degrees.
To find the perimeter of rectangle MNOP, we can use the formula:
Perimeter = 2(length + width)
Since MO is a diagonal and M is 60 degrees and O is 30 degrees, this means that MNO is a right triangle. Thus, we can use trigonometry to find the lengths of MN and NO.
In a right triangle, the side opposite the 30-degree angle is half the hypotenuse (which is MO), and the side opposite the 60-degree angle is √3/2 times the hypotenuse.
Since the length of MO is given as 28 m, we have:
MN = MO * cos(30 degrees) = 28 m * 1/2 = 14 m
NO = MO * sin(30 degrees) = 28 m * √3/2 ≈ 24.2 m
Now, we can calculate the perimeter:
Perimeter = 2(14 m + 24.2 m) = 2 * 38.2 m = 76.4 m
Rounded to the nearest tenth of a meter, the perimeter of rectangle MNOP is approximately 76.4 meters.