The bisector of angle A and D of rectangle ABCD divides side BC into three equal parts by points M and N.

| February 24, 2021 | education

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.



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