In the ABCD rectangle, the bisector of angle A intersects the BC side at point E.

In the ABCD rectangle, the bisector of angle A intersects the BC side at point E. The BE segment is 3 times larger than the EC segment. Find the perimeter of the par-ma if BC = 12cm.

Let EC – x, then BE – 3x. By condition, the entire side BC = 12.
x + 3x = 12
4x = 12
x = 3, we got:
EC = 3 cm, BE = 9 cm.
Now consider the triangle ABE.
In him:
angle BAE = 45 ° (AE is the bisector of the angle BAD),
angle BEA = 180 ° – (90 ° + 45 °) = 45 or 90 ° – 45 ° = 45 °.
Since in triangle ABE two angles are equal, this means that this triangle is isosceles.
AB = BE = 9 cm.
Find the perimeter of the rectangle ABCD by the formula:
P = 2 * (a + b) = 2 * (9 + 12) = 42 cm.
Answer: the perimeter is 42 cm.