The bisector of angle A of rectangle ABCD intersects side CD at point E. It is known that AE

The bisector of angle A of rectangle ABCD intersects side CD at point E. It is known that AE = 4√2, and the perimeter of the rectangle = 20. Find sides.

The bisector AE cuts off a rectangular, isosceles triangle ADE from the rectangle, the hypotenuse of which is 4 * √2 cm.

Then, by the Pythagorean theorem, AD ^ 2 + DE ^ 2 = AE ^ 2.

2 * AD ^ 2 = (4 * √2) ^ 2 = 32.

AD ^ 2 = 32/2 = 16.

AD = 4 cm.

Then AD = BC = 4 cm.

The sum of the sides (AB + CD) = P – (AD + BC) = 20 – 8 = 12 cm.

Then AB = CD = 12/2 = 6 cm.

Answer: The lengths of the sides of the rectangle are 4 cm and 10 cm.