The KM diagonal of the PKME parallelogram divides it into two isosceles triangles with sides 8,8 and 9

univerkov | September 3, 2021 | education

The KM diagonal of the PKME parallelogram divides it into two isosceles triangles with sides 8,8 and 9. Find the perimeter of this parallelogram if the angle between its diagonals HE is 90 °.

By condition, a parallelogram is not a rhombus.

Let РK be the base of the isosceles triangle PE, then PE = KЕ = 9 cm.

In a parallelogram, the lengths of the opposite sides are equal, then ME = PK = 8.8 cm, KM = PE = 9 cm.

Then the perimeter of the parallelogram is: P = 2 * (PK + PE) = 2 * (8.8 + 9) = 2 * 17.8 = 35.6 cm.

Answer: The perimeter of the parallelogram is 35.6 cm.

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