Find the perimeter of the DKIM rhombus if the angle is D = 60 degrees and the diagonal KM = 12 cm.

1. It is known:

a) the sum of the angles of the triangle is 180 °;

b) the sides of the rhombus are equal to each other;

c) the perimeter of the rhombus is 4 times its side;

d) the angles at the base of an isosceles triangle are equal ..

2. In triangle DKM, by the hypothesis of the problem, the side DK is equal to the side DM.

Hence the triangle DKM is isosceles and the angle DKM is equal to the angle KMD.

Let us determine these angles if it is known that the angle D is 60 °.

Angle DKM = angle KMD = (180 ° – 60 °): 2 = 60 °, which means that the triangle DKM is equilateral and the sides of the rhombus are equal to the length of the diagonal KM, which is 12 cm by condition.

3. Calculate the perimeter P of a rhombus with a side of 12 cm.

P = 4 * 12 cm = 48 cm.

Answer: The perimeter of the rhombus is 48 cm.

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