The bisector of rectangle ABCD divides its side BC into parts BK = 10 cm, KC = 5 cm. Find its perimeter.

univerkov | July 25, 2021 | education

Since ABCD is a rectangle, and AK is a bisector of a right angle, then the angle BAK = BAD / 2 = 90/2 = 45.

Then the angle BKA = (180 – 90 – 45) = 45, and therefore the triangle ABK is rectangular and isosceles.

Then AB = BK = 10 cm.

Side length BC = BK + CK = 10 + 5 = 15 cm.

For a rectangle, the lengths of opposite sides are equal, then Ravsd = 2 * (AB + BC) = 2 * (10 + 15) = 50 cm.

Answer: The perimeter of the rectangle is 50 cm.

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