In parallelogram ABCD, the height lowered to the CD side divides it in half and forms an angle

In parallelogram ABCD, the height lowered to the CD side divides it in half and forms an angle of 30 ° with the BC side, AB = 26cm. Find the perimeter of the parallelogram.

Let’s denote the height through ВM. By the property of a parallelogram, the opposite sides are equal, then CD = AB = 26 cm. The height divides the side in half, which means MC = 13 cm. Consider a right-angled triangle BCM. In it, the MBC angle is 30 “, then the hypotenuse is twice the leg opposite to the 30” angle (this is the CM leg), and the side of the parallelogram BC = 2 * 13 = 26 cm is the hypotenuse. P = 2 * (26 + 26) = 104 (cm). It should be noted that this parallelogram is a rhombus (since all its sides are equal).




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