# The perimeter of the parallelogram ABCD is 80 cm. A = 30 °, and the perpendicular

August 31, 2021 | education

| **The perimeter of the parallelogram ABCD is 80 cm. A = 30 °, and the perpendicular BH to the line AD is 7.5 cm. Find the sides of the parallelogram.**

1. A, B, C, D – the tops of the parallelogram.

2. In a right-angled triangle ABH, the perpendicular BH is the leg opposite the angle A, equal to 30 °. Therefore, its length is 1/2 AB:

AB = 2 x 7.5 = 15 cm.

3. To calculate the remaining sides of the parallelogram, we use the formula for calculating its perimeter (P):

P = 2AD + 2AB = 80 cm.

AD = 80 – 2 x 15/2 = (80 – 30) / 2 = 25 cm. BC = AD = 25 cm.

Answer: BC = AD = 25 cm. AB = SD = 15 cm.

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