The smaller side of the rectangle is 5cm. Its diagonals intersect at an angle of 60 degrees. Find the lengths of the diagonals.

1. A, B, C, D – the vertices of the rectangle. ∠АВ = 60 °. О is the point of intersection of the diagonals. AB = 5 cm.

2. Triangle AOB – isosceles, since the diagonals of the rectangle are equal and at the point of intersection are divided into equal segments.


3. Since the sum of the angles of this geometric figure is 180 °, the degree measure of each of them is 60 °, that is, the triangle AOB is equilateral.

Therefore, AB = BO = AO = 5 cm.

Diagonals BD = AC = 5 x 2 = 10 cm.

Answer: diagonals BD = AC = 10 cm.

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