The heights of the parallelogram, drawn from the apex of the obtuse angle, form an angle of 30⁰
| September 26, 2021 | education
The heights of the parallelogram, drawn from the apex of the obtuse angle, form an angle of 30⁰ and are equal to 3 and 5 cm. Find the perimeter of the parallelogram.
In the triangle BCK, the angle СBK = (BCН – KВН) = (90 – 30) = 60.
Then the angle BCК = (90 – 60) = 30.
In a right-angled triangle BCК, the leg BK lies opposite an angle of 30, then BC = 2 * BK = 2 * 5 = 10 cm.
In a parallelogram, opposite angles are equal, then the angle BAН = BCК = 30.
The leg BH of a right triangle is erect against an angle of 30, then AB = 2 * BH = 2 * 3 = 6 cm.
Determine the perimeter of the parallelogram.
Ravsd = 2 * (AB + BC) = 2 * (6 + 10) = 32 cm.
Answer: The perimeter of the parallelogram is 32 cm.
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