# ABCD-rectangle, angle ABM = angle DCM. Find the perimeter of the rectangle if BC = 24cm.

July 28, 2021 | education

| Given:

rectangle ABCD,

point М belongs to the segment BC,

BC = 24 centimeters,

angle ABM = angle DCM.

Find the perimeter of the rectangle ABCD, that is, P ABCD -?

Solution:

1. Consider the rectangle ABCD. Its opposite sides and angles are equal, that is, AB = CD, AD = BC = 24 centimeters.

2. Consider the triangle ABC and BCD. They are equal on both sides and the angle between them, since AB = CD, AD = BC and angle ABM = angle DCM. Therefore AB = CD = AD = BC. Then the rectangle ABCD is a square.

3. Perimeter ABCD, that is, P ABCD = 4 * BC = 4 * 24 = 96 centimeters.

Answer: 96 centimeters.

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