The bisector of angle A and D of rectangle ABCD divides side BC into three equal parts by points M and N.
The bisector of angle A and D of rectangle ABCD divides side BC into three equal parts by points M and N. Side AB is 4. Find the perimeter of the rectangle.
Since ABCD is a rectangle, then CD = AB = 4 cm, AD = BC.
There are two options for the location of the bisectors AН and DM.
Let the bisectors АН and DМ intersect, then BН = AB = 4 cm, since the triangle ABН is isosceles. Since BM = MН = CН, by condition, then BM = BН / 2 = 4/2 = 2 cm, and BC = AD = 3 * BM = 3 * 2 = 6 cm.
Then Ravsd = 2 * (AB + BC) = 2 * (4 + 6) = 20 cm.
Let the bisectors AН and DМ do not intersect within the rectangle, then BН = MН = CM = AB = 4 cm.
BC = AD = 3 * BН = 3 * 4 = 12 cm.
Then Ravsd = 2 * (AB + BC) = 2 * (4 + 12) = 32 cm.
Answer: The perimeter of the rectangle is 12 cm or 32 cm.