In the parallelogram kmnp, the bisector of the angle mkp is drawn, which intersects the side MN at point E

univerkov | March 26, 2021 | education

In the parallelogram kmnp, the bisector of the angle mkp is drawn, which intersects the side MN at point E. Find the side KP of the parallelogram KMNP, if ME = 8 cm, and the perimeter of the parallelogram is 40 cm.

Since the segment KE is the bisector of the angle KMP, it cuts off the isosceles triangle KME, in which KM = ME = 8 cm.

Let the length of the segment EN = X cm, then the length of the segment MN = ME + NE = (8 + X) cm.

Since the opposite sides of the parallelogram are equal, NP = KM = 8 cm, KP = MN = (8 + X) cm.

Then Ravsd = 2 * (KM + KP) = 2 * (8 + 8 + X) = 40 cm.

32 + 2 * X = 40.

X = EN = (40 – 32) / 2 = 4 cm.

Then KP = 8 + 4 = 12 cm.

Answer: The length of the side of the KP is 12 cm.

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