The bisector of the corner of a rectangle divides its side into two parts, each of which is 5 cm.

The bisector of the corner of a rectangle divides its side into two parts, each of which is 5 cm. Find the perimeter.

Since AH is the bisector of the angle ABD, and the angle ABD = 90, then the angle BAН = DAН = ABD / 2 = 90/2 = 45.

Then in the right-angled triangle ABН one of the acute angles is 45, then the right-angled triangle is also isosceles, which means AB = BH = 5 cm.

BC side length = (BH + CH) = (5 + 5) = 10 cm.

Then the perimeter of the rectangle is: P = 2 * (AB + BC) = 2 * (5 + 10) = 30 cm.

Answer: the perimeter of the rectangle is 30 cm.