A straight line is drawn through vertex C of rectangle ABCD, parallel to diagonal BD and intersecting line AD

| January 12, 2021 | education

A straight line is drawn through vertex C of rectangle ABCD, parallel to diagonal BD and intersecting line AD at point K. Through K, a line is drawn parallel to diagonal AC and intersecting line BC at point E. Find the diagonal of the rectangle if the perimeter of ACKE = 24 cm

Line segments CE and DK are parallel because they are continuation of parallel sides of rectangle BC and AD.
Quadrilateral BDCK is a parallelogram (ВС || DK and BD || CK).
BD = CK (1) – opposite sides of the BDCK parallelogram.
Quadrangle ACEK – parallelogram (AC || KE and AK || EC).
AC = KE (2) – opposite sides of the parallelogram ACEK.
AC = BD – rectangle diagonals.
Then AC = BD = CK = KE.
Perimeter AСKE = AC + SK + KE = 3 * AC = 24 cm.
AC = 24/3 = 8 cm.
Answer: AC = BD = 8 cm.



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