The perimeter of the parallelogram is 66 cm. The two corners of the parallelogram are 1: 5
The perimeter of the parallelogram is 66 cm. The two corners of the parallelogram are 1: 5 and the two sides are 2: 9. Find the sides and angles of the parallelogram.
1. Let’s denote one part by x.
2. Let us determine the degree measures of the angles of the parallelogram:
x and 5x.
3. Let’s compose and solve the equation:
5x + x = 180˚;
6x = 180˚;
x = 180˚: 6;
x = 30˚.
4. The degree measure of the smaller angle is 30˚.
5. What is the degree measure of the larger angle?
5 * 30˚ = 150˚.
6. Let’s define the sides of the parallelogram:
2x and 9x cm.
7. Let’s compose and solve the equation:
(2x + 9x) * 2 = 66;
11x = 66: 2;
11x = 33;
x = 33: 11;
x = 3.
8. One part is equal to 3.
9. What is the smaller side of the parallelogram?
2 * 3 = 6 cm.
10. How long is the longer side of the parallelogram?
9 * 3 = 27 cm.
Answer: the angles of the parallelogram are 30˚, 150˚, 30˚, 150˚, and the sides of the parallelogram are 6 cm, 27 cm, 6 cm, 27 cm.