The perimeter of the rhombus is 32cm and one of its corners is 60 degrees. Find the length of the diagonal opposite this corner.

1. The vertices of the rhombus A, B, C, D. ∠A = 60 °. BD is the diagonal. P is the perimeter.

2. The length of each side of the rhombus is P: 4 = 32: 4 = 8 centimeters.

3. ∠А + ∠В = 180 °.

∠В = 180 ° – 60 ° = 120 °.

4. The diagonal of the rhombus also serves as the bisector of the angle from which it is drawn.

Therefore, ∠АВD = 120 °: 2 = 60 °.

5.∠ADB = 180 – ∠ABD – ∠A = 180 – 60 ° – 60 ° = 60 °.

6. In triangle ABD the angles are equal. Therefore, its sides are also equal:

BD = AB = AD = 8 centimeters.

Answer: diagonal BD = 8 centimeters.