ABCD rectangle. AB = 7cm KD = 6cm. BK = bisector of angle ABC. Find Perimeter ABCD.

univerkov | September 21, 2021 | education

Since, according to the condition, BK is the bisector of the angle ABC, then the angle ABK = СBK.

Angle ABC = 90, then angle ABK = CBK = 90/2 = 450.

In a right-angled triangle ABK, one of the acute angles is 45, then its legs are equal to each other. AK = AB = 7 cm.

Determine the length of the side AD of the rectangle AD = AK + KD = 7 + 6 = 13 cm.

For a rectangle, the lengths of the opposite sides are equal.

We calculate the perimeter of the rectangle ABCD

Ravsd = 2 * (AB + CD) = 2 * (7 + 13) = 40 cm.

Answer: The perimeter of the rectangle is 40 cm.

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