In the MNKL trapezoid, the diagonal MK is perpendicular to the side of the KL

| May 14, 2021 | education

In the MNKL trapezoid, the diagonal MK is perpendicular to the side of the KL, the angle NMK = KML = 30 degrees. Trapezium perimeter MNKL = 30cm. Find the side of NK

Since the angle NMK = KML = 30, then the angle NML = 30 + 30 = 60.

In a right-angled triangle MKL, the angle KLM = 90 – 30 = 60. Then the angle NMK = KLM = 60, then the trapezoid is isosceles, NM = KL.

Leg KL lies opposite angle 30, then KL = ML / 2.

Let the length MN = KL = X cm, then ML = 2 * X cm.

The sum of the angles of the trapezoid, with the lateral side, is 180, then the angle NKL = (180 – 60) = 120.

Then the angle MKN = 120 – 90 = 30, then the triangle MNK is isosceles, MN = NK = X cm.

Then Рmnkl = X + X + 2 * X + X = 30 cm.

5 * X = 30.

X = NK = 30/5 = 6 cm.

Answer: The length of the NK side is 6 cm.



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