AO-bisector in an isosceles triangle AEF. Find EF.

It is necessary to solve according to the Pythagorean theorem (it is she who helps us to establish a correspondence between the sides in a right triangle and it says that the sum of the legs is equal to the square of the length of the hypotenuse):

FO ^ 2 = AF ^ 2 – AO ^ 2 = 45 ^ 2 – 36 ^ 2 = 729;

FO = 27;

since EO = OF, then EF = 2 * OF = 2 * 27 = 54;

Answer: 54 dm.