The bisectors of angles A and B at the lateral side AB, the trapezoid ABCD intersect at point F.

The bisectors of angles A and B at the lateral side AB, the trapezoid ABCD intersect at point F. Find AB, if AF = 24, BF = 32

The bisectors BF and AF are drawn from the angles belonging to the lateral side AB, then these bisectors, according to their properties, intersect at point F at a right angle.

Then the triangle AFB is rectangular, in which, according to the Pythagorean theorem, we determine the length of the hypotenuse AB.

AB ^ 2 = AF ^ 2 + BF ^ 2 = 24 ^ 2 + 32 ^ 2 = 576 + 1024 = 1600.

AB = √1600 = 40 cm.

Answer: The length of the lateral side AB is 40 cm.